So I was thinking of asking in the "Ask James Jacobs" thread, did a search there, and found that he's already addressed the issue. Should've looked there first, I guess.
Of course, he's Not A Rules Guy (TM), but since I'm looking at a houserule anyway I'm content to believe that doing things as he describes won't break anything.
You can teleport out of pits created by create pit. While they're extradimensional, they're not extraplanar, and they retain a connection to the world via the entrance that makes teleportation through it possible.
The extradimensional space created by the create pit spells is not a demiplane. It's an extension of whatever plane you're on, and it's physically connected to it. The pit only exists when it's connected in this way, and as such movement in and out of the pit does not bar teleportation and you can still fall into it if you're under a dimensional anchor.
You would absolutely be able to access the bag's contents. Its extradimensional space is entirely portable and contained inside the bag, so as long as you have the bag, you can access its contents. There are certain effects that would prevent this, but create pit is not one of them—if it were, it would specifically mention that in the spell text.
What about this rule?
Fine. If you want things to work that way, go for it.
I don't like that rule. It's basically a fragment left over from early days where the game designers were overly worried about people nesting too many bags of holding inside one another.
Frankly, the create pit spells are ALREADY TOO GOOD in my opinion for their current level. Allowing them to shut down extradimensional spaces or teleport effects goes too far.