1. What would you do if you found out your partner/spouse had falsely accused you of cheating?

I would be more worried that he was thinking about cheating himself, because in my experience, cheaters usually accuse the other half, so they can justify their own thoughts or actions to cheat.

2. Does it matter if he/she knows it's false or genuinely believes there's a chance you cheated?

Yes, it matters if he thinks I have cheated. He should know me, thus should know he trusts me.

3. Does your opinion change if he/she names a specific person and what your relationship to that person is?

In that case, we would be sitting down for a little talk.

4. What if it weren't the first time? (I'll keep this one worded the same.)

I would make an appointment to see a marriage counselor. Repeated false accusations are a sign of trouble.

5. If you are falsely accused, do you believe you have to prove your innocence or the other person has to prove your guilt?

In some cases, I don't think you can prove your innocence. When I was younger, a friend at work thought I had an affair with one of the married auditors. She is still convinced to this day, and I know she won't listen to me when I tell her nothing happened.