As you pointed out, legally it's his home too, however, that doesn't give him the right to use your computer w/o asking, since it is in your bedroom and he currently isn't living there. You have several choices, if the bedroom is your sanctuary, then put a lock on the door, but if you prefer not to do that, then password your computer. Be sure to put all of your private papers, documents, etc., some place safe that he will not get into. Yes, I'm being serious and no, I'm not being dramatic. These guys get curious about us and want to know what we are doing and they do look around.
Have you checked your computer lately to see if he's installed anything on it? He very well may have just been using it for work, but I bet he also was checking things out to see where you've been, etc. Be sure to clear out your cookies after each use. I went down this road many years ago and I'm only trying to warn you of what they can and some of them will do.
You need to think about what boundaries you could put in place about him coming there when you aren't home. BTW, where you expecting him the other day, i.e., he was sitting in the car for a long period of time. Maybe a schedule for visitation, or at least he give you a call to see if it's okay to stop by.
Just my two cents.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.