I think it is fine. If you don't care about the cat, then let it go. I would have just said 'OK'after her first test and left it at that. There is no need for a 'no problem' reply.
Physical separation is better than in house separation IMO. It is just easier. Take the time you are given to work on yourself. Let her be. Let her do her thing. You can do whatever you want now! I recommend staying busy, do something new. Exercise is key. I gym a lot, run a lot, play hockey a lot, am finishing school, taking yoga classes etc.... Don't sit around the house and dwell on things. Become the best man you can. Above else try and detach. It is a wonderful place to be.
I also took time and really thought about our relationship. What was wrong, what was right, what could be fixed, what was my role, what was her role etc. This is important for my future with or without her.
