Yes yes and yes.... Just woke now like it. Its been happening since august frequently which is why I've started on HRT, which to be fair has reduced the severity of it for me.
Best thing to do if you can't go back to sleep in a couple of minutes is get up and do something. If there's been a blast of cortisol or adrenaline to the system it's unlikely you'll go straight back to sleep. Get up, do a chore, read, watch TV, write Xmas cards. It will distract you and hopefully you might be able to get off to sleep again.
I usually can't if it's after 3 which is annoying.