The gym is geared towards the rowers, so lots of ergs, there's a decent variety of weights machines and free weights, some cycling machines (fairly old), and some room in the middle for mats to be put down for core work etc. The end wall is mirrored (with the ergs in front of them), and its generally kept at a good temperature. It is next to the bar though, so there is temptation... :P It's fairly small - if your needs go beyond this you could always go to the gym at Iffley, about a 15 min walk. I'm afraid I can't remember about football teams, but I know there was a group of lads that regularly went to Jowett and had a kick about, and we took part in Cuppers.
15.03 means you'll be on the first floor in Staircase 15, so directly above the JCR/pantry/bar. It was the floor I was on last year - it can be fairly noisy in the evenings but you get used to it, and it does mean you can go to the bar in your slippers... Don't know specifics of the actual room though sorry. You'll be near 3 showers as well.
As far as I know, yes, all rooms have a wash basin with mirror, I can't remember anyone saying that they didn't.