Do Danes use "out" in the same "out of the closet" sense as it can mean in English?
Is 'ude' restricted to 'outside' or can it be used to mean you are out of say a group?
Yes it can
'Ude' can mean 'outside' and, like you said, 'out of a group' or out of the game (ie. when you have lost).
If you want to be clear (and sound more like a Dane) and you mean 'outside' you would say 'udenfor'. The opposite is 'indenfor'.
I have the feeling she is pronuncing "hul". You have to be very careful with Danish pronunciation.
I hear "hul" too but is it correct pronunciation?
The Danish "soft D" can sound a bit like an L, but I think the voice sounds more like soft D than L.
What is the difference between "ud" and "ude"?
Ud means out, ude means outside. Ud- you're going there- can be used with mobile verbs, but ude-you're already there- is immobile. Hope l could explained.