Sure, it is quite understandable. As you have a study room at your home, it is correct just to name the room's name.

First two sentences are correct. Third sentence is not wrong, but it's a bit awkward. Most people would say something like "I use one of the rooms in my house as a study" or "I have 3 bedrooms in my house, but I use one of them as a study"

Yes you can say that. Just like you can say "I'm in my room". Only time it might not work well is if someone doesn't know you call one of your rooms a study.