Aliens vs Predator Collection

Steam doesn't have it listed as a collection in the store, that's why you can't pick it from the giveaway list. If you don't wait for a reply on the ticket, it's ok to create it as base game.

sure you can.
because you give the base game and the winner get dlc`s as a bonus

Yes, you can. You would be giving what is promised (and then some extra) so it's fine.

I sent a ticket about Shogun 2 collection, haven't received an answer in nearly two weeks. You could giveaway the base game and the dlcs to the winner or list them separately (base game, each dlc) or wait for a long time for support to answer.

Sorry about that but i have to do this (because of your typo):
Aliyev vs. Predator!

Was this on sale? :o

You can only make a giveaway if your gift will include the game your giveaway is for, so it's fine to make a giveaway for a base game and give a collection that contains the base game... but it's not fine the other way around.