If I win a giveaway for a game, are my entries withdrawn in other giveaways for the same game?

Nope. Even if you win a game, you're not guaranteed to actually receive it.

Nope.

If you won again you need to tell the giveaway maker of the second one who in turn needs to ask Steamgifts to reroll and select a different winner.

Edit: That's assuming you actually receive the first one which as others are pointing out isn't always 100% guaranteed.

This should NOT be a feature, cause if you happen to encounter a scammer/ someone who didn't understand the site mechanics, and he/she doesn't intend to give you the game, then all your entries would be deleted, and you'd have to re-enter them, BUT by that time those GA-s would probably expire. So nope, this isn't a feature, and you shouldn't wish for this one :)

Good answers, thanks - I've often wondered about this too.

I also had wondered about this as well. What I did when it happened to me is that I manually deleted all of those entries as soon as I activated my won-key (happened yesterday with Rooms.) :)

Well, you can alleviate the issue of a spam/false giveaway by only having the giveaways withdrawn when you mark the game as Received.