For new Q&A sites, does Stack Exchange offer their framework so that other teams can create new sites or is it all in-house?
If you are talking about making your own site outside the Stack Exchange network...
Then yes, you are allowed as long as you:
I think I covered everything, but comment if I didn't.
You can't copyright the look and feel of a site or app. You can patent it, but as far as I know, SE doesn't have any patents (again, comment if I'm wrong).
If you are talking about making another site inside of the Stack Exchange network...
Then yes, you are still allowed :-).
Area51 is where new sites (topics, as you put it) can be suggested.
There is a whole process of them going into private beta, public beta and graduating (or not).
The process is public and community driven - anyone can suggest a new site, so in many ways - nothing is "in-house" (very few exceptions - the original trilogy of Stack Overflow, Super User and Server Fault and Ask Patents, which was a special deal with the US office of patents).