In response to an opponent trying to play a card that requires al of his available resources, can I play to steal one, making him play a different one, or is the cost paid before the card goes on the stack?

Hi!

When you play a card, you've to pay all costs and choose all the targets. Paying is part of the action of "playing" a card, so, you can't use Hate that way.

Moreover Hate doesn't resolve until the stack resolves, so your opponent can play a tactic from his hand (spending all remaining resources) and leave no resources left in his pool when Hate resolves. If this happens, then you do not get the resource since he has none at the time of resolution.

Nevertheless your opponent can play a Tactic that spends all his remaining resources to counter your Hate.