Thank you for taking in a stray. He must have been horribly scared and is lucky to have found such a caring mum.
I agree with Rachelle. Getting him to learn how to use the litter tray would be a good way to work towards stopping the early morning wake up calls, which is probably why he wants to go out. You could also try having a good old rough and tumble play with him just before bedtime, which might tire him out enough to sleep a bit longer. Bear in mind that cats' instincts are to hunt at night, and going out at this time may have been a habit from his straying days. Lots of people use Feliway and love it (expensive - and cheaper online than at the vet), unfortunately it doesn't work for everyone (like me...grrrr.......)
My cats all go to bed when I do, and often sleep later than me - they never wake me up - even Summer, who LOVES being outdoors in her harness and is VERY vocal about it, doesn't start shouting until she knows I'm awake (what a good girl!
), so a routine CAN be established with patience.
Best of luck and thanks again for loving this abandoned puss. Keep in touch.