1. It will not untap. Changing control of a permanent does nothing more than what's "on the tin" -- just changing control.
1b. It isn't entering the battlefield, so enters-the-battlefield triggered abilities will NOT trigger.
2. Mind Control produces a continuous effect that grants control of a creature to Mind Control's controller. If Mind Control leaves the battlefield, that effect ends. Barring other control-change effects, control of that creature will revert to its owner.
3. Nulltread Gargantuan's enters-the-battlefield ability doesn't target. When it resolves, its controller must put a creature they control on top of their library, even if their only creature at the time is Nulltread Gargantuan. (Enters-the-battlefield abilities trigger and resolve after the permanent they're on has entered the battlefield.)
4 and 4.1. You can't sideboard for game 1. If you suspect your opponent has sideboarded for game 1, call a judge.
5. Maelstrom Pulse doesn't damage, enchant, equip, fortify, block, or target the permanents it destroys (with the obvious exception of the permanent actually targetted by the Pulse). Protection covers only those cases, so Maelstrom Pulse is able to destroy something being given protection from one of its qualities if that object wasn't the target of Malstrom Pulse.
6. The converted mana cost of a token is usually zero, since they don't usually have mana costs. One exception is if a token is copying another object -- it'll have the mana cost (and converted mana cost) of the object it's copying.
7. No. The "next end step" will usually be the end step of the current turn. An exception is when a counter is removed from it during an end step; in that case, the trigger will go on the stack at the beginning of the next turn's end step.
7.1. I'm assuming the combat and the spells mentioned in this question are in the same turn; your wording is a bit confusing. After the Lightning Bolt resolves (which is after the Giant Growth resolves), Protean Hydra has no +1/+1 counters and is 3/3. At the beginning of the next end step, when its trigger resolves, it will get eight +1/+1 counters (not ten, since only four counters were actually removed).
You can target Bribery with Swerve. If there is another legal target, you must change it. In a duel (or a multiplayer game where all your other opponents have shroud), there won't be another legal target, since the controller of Bribery isn't his own opponent, so Swerve will resolve doing nothing.
Note that it might still be a bug. Yes, you are forced to target something, but when the ability resolves, MTGO *should* give you a choice as to whether to have your Cyclops deal damage.
Say something to the TO in private; if that makes you uneasy still, say something to the DCI. If you take the latter course of action, make it clear that the TO is unaware of the suspension.
Er... We're both wrong, actually. Indestructible does stop the destruction event from happening; "~ is indestructible" is the same as "~ can't be destroyed." Thus the outside replacement effect has no event to replace.
The situation is then:
When [Guy 2] blocks, [Guy 1]'s triggered ability triggers. When it resolves, since [Guy 2] is indestructible, the trigger does nothing.
When combat damage is dealt, 4 damage is marked on [Guy 1], and the 4 (or more) damage that would be dealt to [Guy 2] is prevented and a +1/+1 counter is removed from [Guy 2].
First I'll make sure I'm understanding your cards correctly:
[Guy 1]
Creature
Trample
[Guy 1] is indestructible.
Whenever [Guy 1] becomes blocked, destroy all creatures blocking it.
8/5
[Guy 2]
Creature
If damage would be dealt to [Guy 2], prevent that damage and remove a +1/+1 counter from [Guy 2].
Situation:
[Guy 1] is attacking. [Guy 2], with four +1/+1 counters, blocks [Guy 1].
A continuous effect is making [Guy 2] indestructible.
A replacement effect says "If [Guy 2] would be destroyed, instead remove two +1/+1 counters from [Guy 2]".
Assuming all this is correct, here is the result:
When [Guy 2] blocks, [Guy 1]'s triggered ability triggers. When it resolves, the replacement effect causes two counters to be removed from [Guy 2] instead of it being destroyed.
When combat damage is dealt, 2 damage is marked on [Guy 1], and the 2 (or more) damage that would be dealt to [Guy 2] is prevented and a +1/+1 counter is removed from [Guy 2].
The damage to the Hydra is prevented (so it doesn't get any wither counters), and two +1/+1 counters are removed from it. Assuming nothing else happens, it'll get four more at the next end step when its third ability's delayed trigger resolves.
Intet, the Dreamer does not change when you can play the card; rather, it tells you that you may play the card from the exile zone.
Cast/activation permissions are tricky. When a continuous effect is telling you that you can play something, it will usually specify either a zone you can play it from that you normally couldn't (in this case, the exile zone), or a time at which you couldn't normally play it (the Flash keyword, for example). The effect only changes what it mentions. That is to say, when it mentions a zone, it doesn't change *when* you can play it, and when it mentions timing, it doesn't change *from where*.
You may choose any optional additional costs when casting something "without paying its mana cost" -- those additional costs aren't the object's mana cost.
A Crystallization in your graveyard is a legal target for Sun Titan's triggered ability. If it would enter the battlefield this way, you'll choose a legal permanent for it to enchant, and this action does not target the chosen creature. You can enchant a creature with shroud this way, and triggered abilities that trigger on that creature becoming the target of something will not trigger.
In the case where Leyline of Anticipation is allowing him to cast planeswalkers while the stack isn't empty, Angel's Grace will still not prevent his Jace or Garruk from being countered. Split second functions only while the card it's printed on is on the stack, and players always receive priority after the top object on the stack resolves.
At the time that Roiling Terrain would begin to deal damage, the game-created planeswalker redirection effect applies to it. If your opponent controls a planeswalker, the game will ask if you want to redirect the damage.
No, since suspend causes you to cast it without paying its mana cost.
1b. It isn't entering the battlefield, so enters-the-battlefield triggered abilities will NOT trigger.
2. Mind Control produces a continuous effect that grants control of a creature to Mind Control's controller. If Mind Control leaves the battlefield, that effect ends. Barring other control-change effects, control of that creature will revert to its owner.
3. Nulltread Gargantuan's enters-the-battlefield ability doesn't target. When it resolves, its controller must put a creature they control on top of their library, even if their only creature at the time is Nulltread Gargantuan. (Enters-the-battlefield abilities trigger and resolve after the permanent they're on has entered the battlefield.)
4 and 4.1. You can't sideboard for game 1. If you suspect your opponent has sideboarded for game 1, call a judge.
5. Maelstrom Pulse doesn't damage, enchant, equip, fortify, block, or target the permanents it destroys (with the obvious exception of the permanent actually targetted by the Pulse). Protection covers only those cases, so Maelstrom Pulse is able to destroy something being given protection from one of its qualities if that object wasn't the target of Malstrom Pulse.
6. The converted mana cost of a token is usually zero, since they don't usually have mana costs. One exception is if a token is copying another object -- it'll have the mana cost (and converted mana cost) of the object it's copying.
7. No. The "next end step" will usually be the end step of the current turn. An exception is when a counter is removed from it during an end step; in that case, the trigger will go on the stack at the beginning of the next turn's end step.
7.1. I'm assuming the combat and the spells mentioned in this question are in the same turn; your wording is a bit confusing. After the Lightning Bolt resolves (which is after the Giant Growth resolves), Protean Hydra has no +1/+1 counters and is 3/3. At the beginning of the next end step, when its trigger resolves, it will get eight +1/+1 counters (not ten, since only four counters were actually removed).
The situation is then:
When [Guy 2] blocks, [Guy 1]'s triggered ability triggers. When it resolves, since [Guy 2] is indestructible, the trigger does nothing.
When combat damage is dealt, 4 damage is marked on [Guy 1], and the 4 (or more) damage that would be dealt to [Guy 2] is prevented and a +1/+1 counter is removed from [Guy 2].
[Guy 1]
Creature
Trample
[Guy 1] is indestructible.
Whenever [Guy 1] becomes blocked, destroy all creatures blocking it.
8/5
[Guy 2]
Creature
If damage would be dealt to [Guy 2], prevent that damage and remove a +1/+1 counter from [Guy 2].
Situation:
[Guy 1] is attacking. [Guy 2], with four +1/+1 counters, blocks [Guy 1].
A continuous effect is making [Guy 2] indestructible.
A replacement effect says "If [Guy 2] would be destroyed, instead remove two +1/+1 counters from [Guy 2]".
Assuming all this is correct, here is the result:
When [Guy 2] blocks, [Guy 1]'s triggered ability triggers. When it resolves, the replacement effect causes two counters to be removed from [Guy 2] instead of it being destroyed.
When combat damage is dealt, 2 damage is marked on [Guy 1], and the 2 (or more) damage that would be dealt to [Guy 2] is prevented and a +1/+1 counter is removed from [Guy 2].
Cast/activation permissions are tricky. When a continuous effect is telling you that you can play something, it will usually specify either a zone you can play it from that you normally couldn't (in this case, the exile zone), or a time at which you couldn't normally play it (the Flash keyword, for example). The effect only changes what it mentions. That is to say, when it mentions a zone, it doesn't change *when* you can play it, and when it mentions timing, it doesn't change *from where*.
You may choose any optional additional costs when casting something "without paying its mana cost" -- those additional costs aren't the object's mana cost.
(Furthermore, even if you could activate abilities as though the card had flash, flash only modifies when you can cast the card anyway.)
(Triggered abilities "trigger", they don't "activate" -- but that terminology incorrectness did not affect the correctness of your conclusions.)
At the time that Roiling Terrain would begin to deal damage, the game-created planeswalker redirection effect applies to it. If your opponent controls a planeswalker, the game will ask if you want to redirect the damage.