What is the null universe?

A universe that contains nothing.

but I believe these answers are outside this universe, which I think of as a simulation being run in some larger context, and thus outside science (and supernatural by definition?).

What do you mean "outside this universe"? Isn't everything inside this universe by definition? If you mean outside the part of the universe that we can interact with, how would it be any different.

I think a lot of this problem is people's inherent tendency to look at plausibility rather than probability. That is, people will accept something if and only if it has a cause. If you watch a movie and a really unlikely event happens, you'll accept it as long as you accepted everything leading up to it.

A particularly interesting example is the idea of an ontological paradox. People normally might think it's weird, but it works, since it caused itself. My reaction is wondering how to calculate how probable it is.

The universe doesn't have a cause, but it doesn't need one. The universe doesn't work that way. What it needs is non-zero prior probability.

By the way, is there a way to see replies to your posts? I thought there wasn't, but it seems unlikely that you've been checking this post every day for the past two years.