1. The good ol' Prisoner's Dilemma! It's classic and has been discussed in great detail in many places. Like here:
Prisoner's dilemma - wikipedia and here:
Prisoner's Dilemma - Stanford Encyclopedia of Philosophy. So I'll say no more about it.
2. This is an interesting one too. One thing that seems to be missing in the puzzle to me, is a surefire way for the billionaire to tell whether you actually intend to drink the toxin or not. I think people get the idea that you can just lie and tell him you do, then actually not drink it and keep the money. But the basic idea of the puzzle seems to be whether you can force yourself to actually intend to do something, knowing that you can change your mind later. If you know you can change your mind, how can you force yourself to actually intend to do it? Anyway, assuming I can't lie, and assuming I can't really intend to drink the toxin without actually drinking it, I would go ahead and drink it. I can't count on faking intention.
More about the puzzle here:
Kavka's toxin puzzle - wikipedia and here:
Dynamic Choice/ Autonomous Benefit Cases - Standford Encyclopedia of Philosophy.