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What does this even mean? If you asked me this should already resolve as false since they have both participated in the election process so far.

This means the focal point thing: whether they will be candidates in the upcoming elections (or whether both drop out). Resolves the day after elections.

It cannot resolve no, because elections have not happened yet. Even if the question had "preelection procedures" instead of "election" - Biden is not even nominated by democratic party at the moment.

I still think it needs more clarification though. What if someone drops out (or dies) but due to technicalities or timing is still on the ballet in at least one state. What if none of them are on the ballet, but at least 1 person still writes in their name?

I use common sense here. If the person is dead - he is not participating. If his his name is not on ballots, then he is not participating.

What if none of them are on the ballet, but at least 1 person still writes in their name?

That is irrelevant to the question, actions of voters do not matter. We can invent infinity of such silly cases. Not even going to start to add them. If you do not understand what the question asks about - you are welcome not to bet.