Dromoka has no effect that makes certain spells other than itself uncounterable, but Spellbreaker Behemoth does. Spellbreaker Behemoth's last ability, being a static ability (C.R. 604.1), has an effect that lasts only while it's on the battlefield (C.R. 611.3b, 113.6, 604.2); during that time, certain spells, including Ulamog, can't be countered; conversely, while it's not on the battlefield, those spells can be countered as normal. The effect applies even if Spellbreaker Behemoth wasn't on the battlefield when the spell was cast, as long as it's on the battlefield while the spell would be countered (C.R. 611.3a-b). On the other hand, Dromoka's last ability doesn't counter any spells that have already been cast and are still on the stack (in this case, Ulamog), but rather keeps certain spells from being cast in the first place.
EDIT (Jan. 5): Editorial; added rule citations.
EDIT (Mar. 19): Clarification.
EDIT (Dec. 19, 2019): Clarification. One rule was renumbered with Core Set 2020.
EDIT (Sep. 24, 2020): Edited; add rule citation.
Only if an effect offers an alternative to the mana cost (using wording like "... without paying its mana cost" or "... rather than pay its mana cost") can you cast Wheel of Fate (C.R. 117.9), since otherwise Wheel of Fate's nonexistent mana cost would be unpayable (C.R. 117.6).
Albeit true, don't the game rules also state that when the active player casts a spell or activates an ability and doesn't explicitly mention that they're holding priority, that the next player in turn order can safely assume that priority has been passed? More specifically, I'm referring to Section 4.2 of the Tournament Rules which states: "Whenever a player adds an object to the stack, he or she is assumed to be passing priority unless he or she explicitly announces that he or she intends to retain it. If he or she adds a group of objects to the stack without explicitly retaining priority and a player wishes to take an action at a point in the middle, the actions should be reversed up to that point."
That is a Magic Tournament Rule, which applies above all to sanctioned tournaments. Compare with C.R. 116.3c, a comprehensive rule, which states that a player with priority who casts a spell or activates an ability "receives priority afterward". But if such a player "delays [his or her] next action", that player chooses not to take any action (whether he or she takes further action depends on the opponent's response), and C.R. 116.3d says that "if a player has priority and chooses not to take any actions, that player passes."
Emrakul's second ability triggers only when you cast Emrakul, not when Emrakul enters the battlefield. Therefore, using Long Road Home won't achieve what you want here, since it doesn't let you cast Emrakul again.
To the Slaughter doesn't prevent players from casting other spells before it resolves. Obsessive Skinner, however, is a creature spell, which you can't normally cast while the stack isn't empty (C.R. 116.1a).
Your opponent can still tap the creature to pay for the crew ability in response to your spell (assuming its power is 1 or greater). Whatever happens to that creature afterwards is irrelevant to the crew ability or its effect (nothing in the crew ability depends on whether the creature remains on the battlefield, for example [C.R. 702.121a]).
You can tap Selvala for mana as you suggest only in very limited circumstances, one of which includes if you bring Force of Savagery onto the battlefield and then pay mana during the resolution of the same spell or ability, provided the spell or ability's effect lets you do so (note that you can activate mana abilities in this circumstance in addition to having priority [C.R. 605.3a, 608.2f]).
Note that Mask of the Mimic has undergone many changes in wording to conform to the current rules. In case of any doubt, consult the Oracle card reference to find a card's wording (C.R. 108.1); in many cases, it's clearer how a card works if you do so. The notable changes in this card include:
The formulation "Sacrifice a creature: Search..." is used on activated abilities (C.R. 602.1), which Mask of the Mimic neither is nor has. The Oracle wording uses an additional cost.
The formulation "search ... for any copy" is obsolete (compare C.R. 706.1); the Oracle wording uses "search ... for a card with the same name".
"Target creature card" is used without including a zone (such as the graveyard) in the description. The Oracle wording uses "target nontoken creature" here, so that a creature on the battlefield is meant (C.R. 109.2).
The formulation "put it into play" is obsolete; the Oracle wording uses "put it onto the battlefield" (C.R. 403.5).
Note that when Verdurous Gearhulk, etc. enter the battlefield under your control during a player's end step, you normally can't tap them for mana with Cryptolith Rite's effect on the same turn -- it's activating an ability with the tap symbol, which you normally can't do if they entered the battlefield this turn (C.R. 302.6). But if they leave the battlefield while their enters-the-battlefield abilities are on the stack, those abilities will still get to resolve (C.R. 113.7a).
You can target Cataclysmic Gearhulk and/or other creatures with Verdurous Gearhulk's ability, even if Verdurous Gearhulk and the other creatures have entered the battlefield at the same time: you put triggered abilities, such as Verdurous Gearhulk's, on the stack the next time a player would get priority, not at the moment they trigger (C.R. 603.2, 603.3). And you can order multiple triggered abilities you control as you wish if they would go on the stack at the same time (C.R. 603.3b).
What if I were to play or target a graveyard Essence Flux with Torrential Gearhulk? Can I return him to hand before he's caught by the cataclysm?
If I counter a spell with Reflector Mage then cast Eerie Interlude and removed the mage, would it remove the countered spell from the game like the old Bone Shredder "bounce" interaction?.
Players sacrifice and choose permanents based on which nonland permanents are on the battlefield when Cataclysmic Gearhulk's ability resolves (C.R. 608.2h). They can't choose or sacrifice permanents that have left the battlefield (by being returned to hand, for example).
Reflector Mage's ability doesn't counter spells (it only prevents certain spells from being cast). However, the effect that keeps certain spells from being cast will last "until your next turn", even after Reflector Mage has left the battlefield before "your next turn" begins (C.R. 611.2a).
EDIT (Mar. 26): Edited first paragraph.
EDIT (Feb. 15, 2021): Edited, including because some rules were renumbered in the meantime.
If you put a legendary permanent named Liliana, Heretical Healer onto the battlefield while you control one or more others, you must have all but one go to the graveyard as a state-based action due to the legend rule (C.R. 704.5j). This will make the ability of the remaining Liliana trigger (assuming that at least one of the other Lilianas isn't a token). When that ability resolves, you must exile that Liliana and return her to the battlefield transformed (it's not optional).
EDIT (Mar. 12): Minor correction.
EDIT (Sep. 28): One rule was renumbered with Ixalan.
EDIT (Mar. 30, 2020): Correctness edit.
Rebound and cascade allow a spell to be cast during the ability's resolution, which is a moment that spells normally can't be cast (C.R. 608.2f). However, any restrictions on casting the spell (such as the one found on Savage Beating) still apply (C.R. 101.2). Therefore, you can't cast Savage Beating with rebound or cascade except during your combat phase.
Sorry I wasn't more clear. Does the attacking creature deal damage to me?
In general, it won't assign (and thus deal) combat damage (C.R. 510.1c, 510.2). One exception to this is if the attacker has trample, in which case it assigns damage to the player or planeswalker it's attacking (in your scenario, you) during the combat damage step (C.R. 702.19c). This answer assumes that your opponent targeted the blocking creature with Impeccable Timing and that creature is destroyed due to the damage from that spell (you wrote only that your opponent casts that spell "in response").
In general, an attacking creature that was blocked but has no blockers won't assign combat damage (C.R. 510.1c), and neither will a blocking creature with no attackers (C.R. 510.1d). One exception to this is if the attacking creature has trample, in which case during the combat damage step, it assigns its combat damage to the player or planeswalker it's attacking if the attacker has no blockers (C.R. 702.19c). This answer assumes that the targeted creature is destroyed due to the damage from Impeccable Timing.
A Vehicle that is also a creature (whether due to the crew ability or otherwise) is affected by anything that affects creatures (C.R. 300.2). For example, Wrath of God would destroy a Vehicle that's also a creature. The crew ability's effect makes the permanent an "artifact creature" without stating any creature types (C.R. 702.122a); this doesn't remove other card types or subtypes it may have (C.R. 205.1b); for example, a Vehicle will remain a Vehicle, since it will still be an artifact (C.R. 205.3g).
EDIT (Jan. 12): Added citation to C.R. 702.121a, which is new to Kaladesh.
EDIT (Oct. 1, 2019; Nov. 3, 2019): Edited to conform to rule change with Throne of Eldraine.
EDIT (Feb. 11, 2022): One rule was renumbered in the meantime.
The answer of yes is grounded in the rules. C.R. 116.2e clarifies that players don't have priority while a spell or ability is resolving. Note also that C.R. 608.2 and 608.3 (which describe how spells and abilities resolve) have no priority window; a player gets priority only after Jace's ability resolves (C.R. 116.3b).
EDIT (Jan. 5): Editorial; added rule citations.
EDIT (Mar. 19): Clarification.
EDIT (Dec. 19, 2019): Clarification. One rule was renumbered with Core Set 2020.
EDIT (Sep. 24, 2020): Edited; add rule citation.
EDIT (Jan. 12, 2019; Jan. 30, 2019): Correctness edit.
That is a Magic Tournament Rule, which applies above all to sanctioned tournaments. Compare with C.R. 116.3c, a comprehensive rule, which states that a player with priority who casts a spell or activates an ability "receives priority afterward". But if such a player "delays [his or her] next action", that player chooses not to take any action (whether he or she takes further action depends on the opponent's response), and C.R. 116.3d says that "if a player has priority and chooses not to take any actions, that player passes."
EDIT: Rephrased post after comment 3 was posted.
You can target Cataclysmic Gearhulk and/or other creatures with Verdurous Gearhulk's ability, even if Verdurous Gearhulk and the other creatures have entered the battlefield at the same time: you put triggered abilities, such as Verdurous Gearhulk's, on the stack the next time a player would get priority, not at the moment they trigger (C.R. 603.2, 603.3). And you can order multiple triggered abilities you control as you wish if they would go on the stack at the same time (C.R. 603.3b).
Players sacrifice and choose permanents based on which nonland permanents are on the battlefield when Cataclysmic Gearhulk's ability resolves (C.R. 608.2h). They can't choose or sacrifice permanents that have left the battlefield (by being returned to hand, for example).
Reflector Mage's ability doesn't counter spells (it only prevents certain spells from being cast). However, the effect that keeps certain spells from being cast will last "until your next turn", even after Reflector Mage has left the battlefield before "your next turn" begins (C.R. 611.2a).
EDIT (Mar. 26): Edited first paragraph.
EDIT (Feb. 15, 2021): Edited, including because some rules were renumbered in the meantime.
EDIT (Mar. 12): Minor correction.
EDIT (Sep. 28): One rule was renumbered with Ixalan.
EDIT (Mar. 30, 2020): Correctness edit.
EDIT (Feb. 15): Correctness edit; added rule citations.
EDIT (Feb. 17, 2018): Further correctness edit.
EDIT (Feb. 15): Correctness edit.
EDIT (Feb. 17, 2018): Further correctness edit.
EDIT (Jan. 12): Added citation to C.R. 702.121a, which is new to Kaladesh.
EDIT (Oct. 1, 2019; Nov. 3, 2019): Edited to conform to rule change with Throne of Eldraine.
EDIT (Feb. 11, 2022): One rule was renumbered in the meantime.