Wondering how wordpress Answers works? I like it!
This site is part of the Stack Exchange network of Q&A sites. New sites can be proposed via the Area51 site. There is already a LGBT proposal, but it needs more work to define the scope. A (maybe) related proposal, Everything You Always Wanted to Know about Sex but were Afraid to Ask, is already in the next stage.
The network runs on software and servers from stack overflow internet services inc., but there are open source alternatives that you can run yourself.