I have an extremely curious question relating to time-travel paradoxes which I believe has not been thought of before. Can I ask it in the main site?
You can ask questions on time travel in the framework of relativity or some other accepted theory, but you can't just ask about "time travel" in general. You need to be working in the framework of some theory. If it has absolutely nothing to do with an accepted theory in physics, it might still be relevant on the scifi stackexchange. If your question starts out with, "say you have a time machine", it probably isn't a good fit for physics stackexchange.
That's not to say that if you ask it, it will be voted up. There are are a lot of questions on this site about the "paradoxes" of special relativity already.