Last night me and my family went to a party (my aunt's 50th) and came back late at around 1 AM. I went to bed at around 2 AM, and thought I might as well try a WILD as it was in the early hours of the morning. I was surprised that it worked very well, having heard that it was normally only achievable after a few hours' sleep.

Would I have still had a REM phase at 2 in the morning, having not slept before?
Do other people have successful WILDs after not sleeping, just going to bed late instead?
I haven't been able to do a WILD when going to bed at normal time (along with most people) but do REM stages still happen at the same times when you're awake?