1/2 - I'd just get a hotel. I wouldn't think Sunday night near ORD should be all that bad. xmas shoppers would screw up hotels in the city, not as much by ORD and also on Fri/Sat, not as much on Sun. Even if room isn't ready, you should be able to drop bags. You might be best to find something close to one of the Blue Line stations (Rosemount or Cumberland). If you get a hotel not near that, you'll have to ride to ORD postgame and then get the shuttle.
3 - sorry, can't help on this one
4 - Blue Line runs 24/7. Some trains short turn at UIC/Halsted (2 stops east of Illinois Medical District, the stop closest to the UC), so your wait may be a little longer on the way back. If you get a UIC/Halsted train going in, just take it, get off at Halsted when they kick you out and then wait for the next train which should take you the last two stops to IMD.

You will get razzed for wearing a Canucks jersey, especially if it's a Sedin