"When are you collecting me?" was not accepted. This is wrong. My Danish family use this word all the time to mean 'collect'
Can you collect one person from somewhere? I only know that as "pick up".
I also think "when are you collecting me" should be accepted.
Can you "Henter en pige på klubben?"... pick up a girl at the club?
No, 'at hente' only means to pick someone up physically in a car or to meet them and follow them home.
To pick someone up at a club, you would use 'jeg scorer en pige/fyr på klubben' or 'jeg får en pige/fyr med hjem' (bring a girl home)