My thoughts about this site

You can do that.

You can do that, kinda.

You can always make a file in dropbox or upload a file to somewhere with the puzzle, and give the group the link to the file.

You can do that and also group giveaways. If you're part of a Steam group and someone in that group makes a giveaway, you will see it on the list.

In theory you can make it private to an extent. When you start a Giveaway you can set it so that only people who have the link to the Giveaway can enter. Obviously someone can just copy paste all over the place, but the point is that it doesn't make the giveaway public.