[Respectfully snipped] The floor cleaner bothers me too. IMO, JA arrived at 4AM, parked around the corner, watched TA cleaning the floor (OR maybe he was sound asleep upstairs), she waits for the right moment and sneaks into the house. Her goal at this point is to creep on his computer, possibly uploads or copies TA's hard drive.
I think the computer activity at 4AM is JA, doubtful TA would use a proxy server to watch the same music video 3x. I can come up with two reasons JA would use a proxy server: A) to conceal whatever she was doing on the, just covering her tracks, or B) installation of keylogger software. Why would she lie about where she parked upon "official" arrival (probably late morning)? Too many lies to keep up with, IMO. She did not park her car in the middle of the driveway at 4AM because she was in stealth mode, and obviously TA's roommates would see a random car when they left in the morning, which they did not.