privacy on someone else's wirelss.

If I use someone's wireless connection, can they see all the web sites I go to? Do they have to have to be signed on at the same time to see my activiity or is there a running history of all sites visited on that particular wireless?
If there is a list, how long does the history last? Can someone see activity that was on their wireless from a few months ago?
Lastly, do places that provide wireless for inhabiatants like dorms, apartments, housing places check up on what sites are being visiited? Or do they generally ignore it unless they have reason to check up on something?

yeah yeah I know I sound paranoid. Trust me, I just know very little about how all this works and have wondered these questions for a while until I found this forum.
Thanks in advance for your answers.