It may have a nest there and that could explain it (and possibly the squeaking), however in my experience, mice will tend to stay in the general area of the house that they occupy. The fluttering you explain is interesting, could be a mouse, or something else(?). We had a mouse problem in our old house and it was just crazy. I agree that if you hear one (it could even be more than that) then you may soon find out you have a lot more
We had to finally set up traps and never found how they were getting into the house. They can squeeze into amazingly small spaces and proliferate rapidly.
Hopefully it got into the house by fluke
and will find it's way out (and no more come in). You might want to do a check for any areas around the outside of the house that a mouse could be getting into, just in case.
You could also try setting a live trap up with some cheese or peanut butter inside to try and attract it out, then release it far from the house.