The ability still works like normal. All non-Horrors with a slime counter will lose their abilities and will be 2/2s, Sludge Monster included. The Monster losing its abilities from its own ability doesn't stop its ability from working, since it's already been applied.
During each step and phase, the active player gets priority first, then the nonactive player gets priority. That means the active player gets the first chance to act, and if they pass priority and the nonactive player passes priority back without doing anything, then we move on to the next step or phase. For example, if the attacking player is holding a Giant Growth and they want to cast it, they'll have to do so after blockers are declared, but before knowing if the nonactive player is going to do anything (because if they pass to the opponent, and the opponent passes back without doing anything, we move on to the combat damage step before the active player can cast the Growth).
No you may not. You only have access to the back side if you're playing or casting it. If you're putting it onto the battlefield, then you only look at the front side, and the front side of the Recovery is a sorcery, not a land, so you cannot put it onto the battlefield back face up.
The triggered ability from persist goes on the stack above the Time trigger and resolves first. The Finks will return to the battlefield first, then, if it's still on the battlefield when the Time's trigger resolves, it will be phased out.
If you target the Gravecrawler you sacrificed to activate the ability, when the ability goes to resolve, it sees its only target is now illegal and the entire ability does nothing (so you will not draw a card). If you wanted to draw a card, you would need to target a different creature or choose zero target creatures (since it says "up to one", you can choose zero targets if you want).
1. Yes, if Thoughtseize is countered, none of its effects will happen. The other player won't discard and the player who cast Thoughtseize won't lose any life.
2. Yes, they'll still lose 2 life, even if the targeted player has no cards that can be discarded.
The effect that prevents the creature from untapping is set up by the enter the battlefield trigger resolving. The Geist losing its abilities won't do anything, since they still control the Geists. So no, playing the Transformation on the Geists does not mean that the targeted creature will untap now, since the Geists are still on the battlefield.
Once Tooth and Nail are done resolving, there are two triggers waiting to go on the stack - the Chancellor trigger and the Behemoth trigger. Since you control them both, you get to choose the order they're put on the stack. If you put the Chancellor trigger on the stack last, it will resolve firsti, so you'd get 3 tokens, then the Behemoth would give all of your creatures +6/+6.
There is nothing in the rules that says a noncreature can't have deathtouch (for example, Pestilent Spirit gives instants and sorceries deathtouch). So there's nothing preventing a planeswalker from having deathtouch. If a planeswalker has deathtouch. If a planeswalker has deathtouch and uses an ability that deals damage to a creature, the damaged creature will be destroyed. Just note that deathtouch requires 1 or more damage dealt to work - dealing zero damage is the same as not dealing any damage at all.
You can activate the ability as many times as you want, as long as you can pay the cost. If you have six mana, you can activate it twice to give it a total of +6/+6.
It triggers at the beginning of your precombat main phase. That only happens once each turn. A triggered ability will trigger each time the trigger condition becomes true. Your precombat main phase only happens once each turn, so the ability will only trigger once. It doesn't keep triggering because you want it to trigger multiple times
603.2b When a phase or step begins, all abilities that trigger “at the beginning of” that phase or step trigger.
The Heir is completely different. It has an activated ability, and normally, you can activate an ability as many times as you want to as long as you can pay the cost. But the Heir has a restriction on its use (to restrict how many times you can use it to free discard), so you can only activate it once (and then it transforms). But that is not how triggered abilities work. They only trigger when their condition becomes true.
Cards do what they say. If a card doesn't say to do something, then it doesn't do that.
The Regent says that the creature won't untap as long as you control the Regent, so that's what it does - taps the creature and prevents it from untapping as long as the Regent is in play. Frost Lynx doesn't say that - it just says to tap the creature and that the creature won't untap during its controller's next untap step. So the creature will not untap once, and will then untap like normal, whether or not the Lynx is still on the battlefield. If it stayed tapped as long as the Lynx was on the battlefield, then it would be worded like the Regent.
No it would not. It doesn't have the dies trigger thank to Frogify, so if the God dies with Frogify attached to it, it will go to the graveyard and stay in the graveyard.
"Dies" is only used for creatures or planeswalker - it's not designed to be a catch all for anything that goes to the graveyard from the battlefield. For instance, cards like Brought Back and Retributive Wand don't use the word "die" or "dies" either.
Mirri only affects creatures that are declared as attacker. It won't do anything about creatures that are put onto the battlefield attacking. So yes, you'll get your 10 tokens, and they will be tapped and attacking.
2. Yes, they'll still lose 2 life, even if the targeted player has no cards that can be discarded.
The Heir is completely different. It has an activated ability, and normally, you can activate an ability as many times as you want to as long as you can pay the cost. But the Heir has a restriction on its use (to restrict how many times you can use it to free discard), so you can only activate it once (and then it transforms). But that is not how triggered abilities work. They only trigger when their condition becomes true.
The Regent says that the creature won't untap as long as you control the Regent, so that's what it does - taps the creature and prevents it from untapping as long as the Regent is in play. Frost Lynx doesn't say that - it just says to tap the creature and that the creature won't untap during its controller's next untap step. So the creature will not untap once, and will then untap like normal, whether or not the Lynx is still on the battlefield. If it stayed tapped as long as the Lynx was on the battlefield, then it would be worded like the Regent.