Yes, disabled parking is everywhere, and is usually very close (except for MK/TTC - there's still a long walk even from the disabled parking), follow the signs and the blue lines on the ground. The exception is Epcot right now, as you will want to go in the FIRST lot, and all the way to the front disabled parking area. Do NOT enter the second lot. The normal short entry path from the second lot is closed, so you will have to walk all the way back to the main parking lot entrance. It's very stupid and they don't tell you this.
No trams are running that I have seen yet.