There doesn't seem to be any reason why I should be experiencing these specific qualia instead of others, that I "popped into existence" as this specific consciousness instead of another, or that I perceive time subjectively. 

..assuming that the I is separable from memories and experiences. Otherwise, you are what you are..

Based on what I know, and that qualia occur, what is the probability (if any) that I will pop into existence again and again, and experience different qualia each time, with no subjectively perceivable connection with the "previous" consciousness?

That still requires the separate I assumptions. Otherwise, it is no different from a bunch of different people experiencing different things.

does suffering have a limit or is it infinite? 

If suffering is infinite, likely joy is too. Why not let the infinities cancel out?