2: Goblin Cannon deals 1 damage to any target. Sacrifice Goblin Cannon.
After you activate this ability, it doesn't resolve right away but goes onto the Stack. You will receive priority after activating it. With that priority, you can activate abilities, so because this is an activated ability, you can activate this again.
Those three things are stated in rules 602.2 ("To activate an ability is to put it onto the stack and pay its costs, so that it will eventually resolve and have its effect."), 117.3c ("If a player has priority when they cast a spell, activate an ability, or take a special action, that player receives priority afterward."), and 117.1b ("A player may activate an activated ability any time they have priority.").
Just activate Goblin Cannon as many times as you want to use it. Even after sacrificing Goblin Cannon, it will deal the damage to the targets if they are legal:
113.7a Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won’t affect the ability. Note that some abilities cause a source to do something (for example, “Prodigal Pyromancer deals 1 damage to any target”) rather than the ability doing anything directly. In these cases, any activated or triggered ability that references information about the source for use while announcing an activated ability or putting a triggered ability on the stack checks that information when the ability is put onto the stack. Otherwise, it will check that information when it resolves. In both instances, if the source is no longer in the zone it’s expected to be in at that time, its last known information is used. The source can still perform the action even though it no longer exists.
Your opponent might be able to destroy or remove any of the Auras that are attached to Three Dog in response to its attack trigger. You will get the option to sacrifice any one Aura that does remain attached to Three Dog at the time the ability resolves. If all the Auras were removed you can't sacrifice one, but any that are attached are still there to sacrifice, and will trigger the reflexive trigger. At that stage, there is no way to disrupt the ability except to counter it, as it is only an instruction to create some tokens copying some Last Known Information.
303.4h If an effect attempts to put a permanent that isn’t an Aura, Equipment, or Fortification onto the battlefield attached to an object or player, it enters the battlefield unattached.
The token copy of the Eidolon is not a bestowed Aura, so the instruction to put that permanent onto the battlefield gets edited to become the instruction to just put that token onto the battlefield unattached. You make essentially a token copy of Eidolon of Countless Battles for each other attacking creature you control.
You can't apply both alternative costs when using the escape on the cards in your graveyard. Choosing to use escape means choosing to pay the escape cost instead of the mana cost.
702.138a Escape represents a static ability that functions while the card with escape is in a player’s graveyard. “Escape [cost]” means “You may cast this card from your graveyard by paying [cost] rather than paying its mana cost.” Casting a spell using its escape ability follows the rules for paying alternative costs in rules 601.2b and 601.2f–h.
Fires of Invention now cannot also allow you to duck paying the mana cost because you've already substituted for the mana cost. (601.2b) If you want to escape, you have to pay the escape cost.
The mana value of the spell is not dependent on additional costs to cast the spell, including the so-called Commander Tax. Mana value is a calculation of the symbols appearing in the mana cost characteristic, in the upper-right corner. Mana value is just the total amount of mana equivalent to those symbols, ignoring color (CR202.3). The mana you pay to cast the spell may depend on the mana cost, but the mana value does not depend on the mana you pay to cast the spell.
608.2. If the object that’s resolving is an instant spell, a sorcery spell, or an ability, its resolution may involve several steps. The steps described in rules 608.2a and 608.2b are followed first. The steps described in rules 608.2c–k are then followed as appropriate, in no specific order. The steps described in rule 608.2m and 608.2n are followed last.
[...]
608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process. If all its targets, for every instance of the word “target,” are now illegal, the spell or ability doesn’t resolve. It’s removed from the stack and, if it’s a spell, put into its owner’s graveyard. Otherwise, the spell or ability will resolve normally. Illegal targets, if any, won’t be affected by parts of a resolving spell’s effect for which they’re illegal. Other parts of the effect for which those targets are not illegal may still affect them. If the spell or ability creates any continuous effects that affect game rules (see rule 613.11), those effects don’t apply to illegal targets. If part of the effect requires information about an illegal target, it fails to determine any such information. Any part of the effect that requires that information won’t happen.
The 2 damage dealt to Psi Blast's controller is dependent on the spell resolving, which it doesn't do if all of its only target becomes illegal. The spell fizzles.
It doesn't "double or set to a specific value" your life total, so we judge half of your life as -10/2 = -5, but it is a "calculation that would determine the result of an effect", so when it yields -5, zero is used instead. You lose 0 life, which is to say, nothing happens.
Miirym creates tokens that are copies, it doesn't copy spells. The note about copying information about how the spell was cast only applies if you copy a spell. See CR 707.2.
If Zacama enters the battlefield when Miirym and the Maskwood Nexus are there, then Miirym triggers, and creates a token that's a copy of Zacama except it's not legendary. The token's ability from Zacama does not trigger because you did not cast that token; it was never a spell, you created it on the battlefield.
First, it's important to state that Char-Rumbler has printed power -1, and based on this and rule 208.4b, it may be considered to have base power -1. The printed power is a value that factors in to determining what the object's power is, along with effects that apply to that card, and this rule:
107.1b Most of the time, the Magic game uses only positive numbers and zero. You can’t choose a negative number, deal negative damage, gain negative life, and so on. However, it’s possible for a game value, such as a creature’s power, to be less than zero. If a calculation or comparison needs to use a negative value, it does so. If a calculation that would determine the result of an effect yields a negative number, zero is used instead, unless that effect doubles or sets to a specific value a player’s life total or the power and/or toughness of a creature or creature card.
The card's power is treated as either -1 or 0, depending on who's asking. You use 0 at the point that something would actually happen. The magnitude of an effect is positive or zero. Otherwise, for a "calculation or comparison", the real negative value is used.
We would also say that the card can't assign negative combat damage, zero is used instead. Refer to the rules for the combat damage step, which explain:
510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power. Creatures that would assign 0 or less damage this way don’t assign combat damage at all.
When Worldspine Wurm is put into a graveyard from anywhere, shuffle it into its owner's library.
triggers from the same event as the Enduring Renewal one, if Worldspine Wurm dies. They both go to the Stack, but, when one of them resolves, it moves the Wurm to where the other can't find it. You can choose to put the Enduring Renewal ability on top of the one from the Wurm, and it will resolve first, moving WW into your hand.
Yes, Prosperous Innkeeper is on the battlefield under that player's control at the time the other creatures enter the battlefield, its ability triggers for all the other creatures that enter the battlefield that way. (CR603.6a)
On this card and all others, "109.2. If a spell or ability uses a description of an object that includes a card type or subtype, but doesn’t refer to a specific zone or include the word “card,” “spell,” “source,” or “scheme,” it means a permanent of that card type or subtype on the battlefield."
Because the Skydiver just says 'artifact', it means an artifact permanent - which is not an artifact card in your graveyard. You can't target a card in your graveyard.
The player who owns the token is the player who creates the token (CR111.2), which is able to differ from the player under whose control the tokens are created, by means of effects of precisely this sort. This effect changes the controller but doesn't say it changes who does the creating, so it's still whoever the other effect says creates the tokens. That player is the one who owns them.
2: Goblin Cannon deals 1 damage to any target. Sacrifice Goblin Cannon.
After you activate this ability, it doesn't resolve right away but goes onto the Stack. You will receive priority after activating it. With that priority, you can activate abilities, so because this is an activated ability, you can activate this again.
Those three things are stated in rules 602.2 ("To activate an ability is to put it onto the stack and pay its costs, so that it will eventually resolve and have its effect."), 117.3c ("If a player has priority when they cast a spell, activate an ability, or take a special action, that player receives priority afterward."), and 117.1b ("A player may activate an activated ability any time they have priority.").
Just activate Goblin Cannon as many times as you want to use it. Even after sacrificing Goblin Cannon, it will deal the damage to the targets if they are legal:
113.7a Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won’t affect the ability. Note that some abilities cause a source to do something (for example, “Prodigal Pyromancer deals 1 damage to any target”) rather than the ability doing anything directly. In these cases, any activated or triggered ability that references information about the source for use while announcing an activated ability or putting a triggered ability on the stack checks that information when the ability is put onto the stack. Otherwise, it will check that information when it resolves. In both instances, if the source is no longer in the zone it’s expected to be in at that time, its last known information is used. The source can still perform the action even though it no longer exists.
The token copy of the Eidolon is not a bestowed Aura, so the instruction to put that permanent onto the battlefield gets edited to become the instruction to just put that token onto the battlefield unattached. You make essentially a token copy of Eidolon of Countless Battles for each other attacking creature you control.
702.138a Escape represents a static ability that functions while the card with escape is in a player’s graveyard. “Escape [cost]” means “You may cast this card from your graveyard by paying [cost] rather than paying its mana cost.” Casting a spell using its escape ability follows the rules for paying alternative costs in rules 601.2b and 601.2f–h.
Fires of Invention now cannot also allow you to duck paying the mana cost because you've already substituted for the mana cost. (601.2b) If you want to escape, you have to pay the escape cost.
[...]
608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process. If all its targets, for every instance of the word “target,” are now illegal, the spell or ability doesn’t resolve. It’s removed from the stack and, if it’s a spell, put into its owner’s graveyard. Otherwise, the spell or ability will resolve normally. Illegal targets, if any, won’t be affected by parts of a resolving spell’s effect for which they’re illegal. Other parts of the effect for which those targets are not illegal may still affect them. If the spell or ability creates any continuous effects that affect game rules (see rule 613.11), those effects don’t apply to illegal targets. If part of the effect requires information about an illegal target, it fails to determine any such information. Any part of the effect that requires that information won’t happen.
Emphasis added.
If Zacama enters the battlefield when Miirym and the Maskwood Nexus are there, then Miirym triggers, and creates a token that's a copy of Zacama except it's not legendary. The token's ability from Zacama does not trigger because you did not cast that token; it was never a spell, you created it on the battlefield.
107.1b Most of the time, the Magic game uses only positive numbers and zero. You can’t choose a negative number, deal negative damage, gain negative life, and so on. However, it’s possible for a game value, such as a creature’s power, to be less than zero. If a calculation or comparison needs to use a negative value, it does so. If a calculation that would determine the result of an effect yields a negative number, zero is used instead, unless that effect doubles or sets to a specific value a player’s life total or the power and/or toughness of a creature or creature card.
The card's power is treated as either -1 or 0, depending on who's asking. You use 0 at the point that something would actually happen. The magnitude of an effect is positive or zero. Otherwise, for a "calculation or comparison", the real negative value is used.
We would also say that the card can't assign negative combat damage, zero is used instead. Refer to the rules for the combat damage step, which explain:
510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power. Creatures that would assign 0 or less damage this way don’t assign combat damage at all.
triggers from the same event as the Enduring Renewal one, if Worldspine Wurm dies. They both go to the Stack, but, when one of them resolves, it moves the Wurm to where the other can't find it. You can choose to put the Enduring Renewal ability on top of the one from the Wurm, and it will resolve first, moving WW into your hand.
Because the Skydiver just says 'artifact', it means an artifact permanent - which is not an artifact card in your graveyard. You can't target a card in your graveyard.