Sometimes the best thing to do is to face your fears head on. I had a lot of the same fears when my husband first started dating his gf. I'm still not comfortable with them having sex in the house when I'm home (but then again I'm not comfortable with anyone having sex in my house while I'm in it if it's not me). I don't have any desire to know when or where or how often they are intimate, as long as it's not impacting my sex life it's all good.
As for them going out and me being alone at home, I've got to the point that I quite enjoy it. I like that he has someone to go out with to do stuff with that I'm not interested in. It takes the pressure off.
If you think you like her and think that she might be good for him it might be a good idea to let go a little. Chances are he'll surprise you in a positive way. You're worst case scenario isn't likely to happen. Also you're probably not going to be ok with things overnight. It's going to take a lot of talking and things that have been just below the surface of your relationship are going to come up and have to be dealt with. Ride the ups and downs, they do smooth out.
Everything will be ok in the end. If it's not ok it's not the end.