How long should I wait on a fight thread?

I think that becomes more a matter of personal preference. I tend to tap people if I notice my threads have gone 2 weeks without a reply, but the character hasn't been swept by the activity checker. At that point I just assume they've forgotten about our thread and send them a quick PM to check in and see where we're at.

In your example, where the outcome of Thread A directly effects the outcome of Thread B, I think that's really up to you and whether or not you're comfortable sending a PM out. Sometimes a quick PM to let someone else know the thread you have together is important for your character's storyline is enough to spur the other player back into action or to discuss the outcome and continue accordingly.

To my knowledge, there's no "official" timeout for non-aggressive spars, but that might be a better question for @WOLF.

Edit: Shadow posted. What Chels said.