when we play tidebinder, our opponent's soul warden will trigger. can we counter this trigger with our tidebinder?

only on our opponent's turn.

both triggers will happen at the same time. so they will attempt to be put onto the stack at the same time. however because they are different players' triggers, they are put onto the stack in apnap order.

we also need to know that we choose targets as the trigger is being put onto the stack.

It depends on whose turn it is.

When multiple players would draw cards, those cards are draw in APNAP order, i.e. the active player (whose turn it is) draws their cards first, then the next player in turn order, and so on.

When Words of Waste (or any other effect) replaces a draw with something else, that replacement effect happens when you would have drawn the card.

So, if it’s your turn then your opponents will discard before they draw any cards, but if it’s the turn of another player, then some will have drawn cards before they discard and others won’t have. If you only just finished your own turn, then everyone else will have drawn before they have to discard.

It depends on whose turn it is. When multiple players have triggered abilities that trigger from the same event, those triggers go on the stack in APNAP order. This means that the player whose turn it is puts their triggers on the stack first, then the next player puts their triggers on the stack, and so on. The stack resolves last-in, first-out, so in a two player game the player whose turn it isn't will be the one who has the first option to imprint the creature onto their Mimic Vat. If that player chooses not to imprint the creature, then the active player gets the option. If neither player chooses to imprint the creature, then it stays in its owner's graveyard.

When Patron's trigger destroys the creature, both its ability and Athreos's ability will trigger. Patron of the Vein's trigger goes on the stack first, since it's your turn, and then Athreos's trigger goes on the stack above it. When Athreos's trigger resolves, you can either pay life to keep the creature in the graveyard or you can let it return to your opponent's hand. No matter which option you choose Patron of the Vein's trigger will still resolve and do as much as it can. Even if you let the creature card return to your opponent's hand, Patron of the Vein will give all of your vampires a +1/+1 counter.

The triggers’ controller always chooses their relative order. 

It depends on whose turn it is.

Whenever a player casts a spell from their hand, both Possibility Storm and Knowledge Pool will trigger, but the order of those triggers depends on whose turn it is.

If it’s your turn:

 Your Knowledge Pool’s trigger goes on the stack first, with your opponent’s Possibility Storm’s trigger above it on the stack. 

Possibility Storm’s trigger resolves first, exiling the spell and other cards until a card of the same type is revealed and cast (or not). All cards revealed this way that weren’t cast (including the original spell) are put on the bottom of its owner’s library in a random order. 

The spell cast from Possibility Storm’s trigger resolves next. 

Knowledge Pool’s trigger goes to resolve but does nothing. The spell that triggered Knowledge Pool is no longer on the stack, so it can’t be exiled and thus the trigger has no effect.

If it’s your opponent’s turn:

Your opponent’s Possibility Storm trigger goes on the stack first, with your Knowledge Pool trigger on the stack above it. 

Knowledge Pool’s trigger resolves first, exiles the spell, and allows the spell’s controller to cast another nonland card exiled by Knowledge Pool. 

The spell cast off of Knowledge Pool resolves next.

Possibility Storm’s trigger resolves. The spell that triggered it is no longer on the stack, so it can’t be exiled, but that doesn’t matter since doing so isn’t required for Possibility Storm to have its full effect, unlike Knowledge Pool. The game remembers how the original spell looked as it last existed on the stack and uses that information when revealing cards and looking for a new spell to cast (or not.) All cards revealed this way that aren’t cast are put on the bottom of their owner’s library in a random order.

Finally, the spell cast of Possibility Storm resolves.