I believe the planes' owner choses the order of the planes they put on the bottom of their planar deck. In a game using a shared planar deck though, the planar controller (typically the active player) is considered the owner of all the planes, so they will decide the order as Rhadamanthus stated. Note that when playing with each player using their own planar decks, Norn's Seedcore can result in multiple planes owned by multiple players all being active at the same time, as chaos can ensue during any player's turn.

Yes, they can do that.

From Gatherer: 10/4/2004 This is a life loss and not a life payment so you can bid more life than you have.

Regarding Phyrexian Unlife there are a couple other things going on here. First is that Illicit Auction causes loss of life rather than dealing damage. That means even if their life total was already 0 or less they could still bid 1000 life without worrying about poison, since only damage will cause them to receive poison counters.

If something were to cause your opponent to take 1000 damage all at once (such as a massive attack or very large Fireball) they would go to -980 with no poison counters due to all the damage being dealt while they had more than 0 life.

From Gatherer: 6/1/2011 Phyrexian Unlife won't affect damage that reduces your life total from a positive number to 0 or less. For example, if you're at 3 life and are dealt 5 damage, you'll end up at -2 life. The next time you're dealt damage, it will be dealt as though its source had infect.

Gyrus, Waker of Corpses second ability creates a delayed triggered ability. If you end the turn before that ability triggers, it will still trigger the next time the applicable condition is met. That is, if you activate Sundial of the Infinite before the end of combat step on the turn you create the token, the ability will trigger to exile the token during your opponent's end of combat step on the next turn.

If you wait for the ability to trigger (which is what you most likely want to do anyways so that combat damage is dealt) and end the turn during your end of combat step, the ability will be exiled and fail to resolve, so you'll keep the token. Since it already triggered, it won't trigger again. If the ability was granted to the creature (such as if Gyrus said "It gain's "Exile this token at end of combat"") that ability would trigger at ever end of combat step rather than just once. As written though, you'll keep the token.

TL;DR - Yes, you can use Sundial of the Infinite to "Stifle" the exile and keep the token.