Yes, noise is not a problem. And LHR has a curfew, so flights end before midnight and only start up again at 5:30 or 6am.

You should be in your bed -- if that's where you want to be -- by 9:30pm. Next morning you can do a landside bus transfer from T4 to T1, or go down to the Heathrow Express and use it for free to get to T1. The Tube requires you to buy a ticket to ride it between T4 and LHR Central [T1,2&3].