Is it possible to ga Origin keys?

Nope.

Nope. It's steamgifts, not origingifts, so they can't check if the winner actually activated the game. Just try to trade it or gift it to someone.

Have you Googled Origin giveaway groups?

You can still create a contest or something like that if you want.
But you can't create a regular giveaway.

It was once actually possible to give away Battlefield 3 (and Minecraft) on SteamGifts, as those two games were granted exceptional status due to popular demand, but the practice was discontinued almost 4 years ago.

no only Steam !
But you can give it here in Discussions away and make a liitle Puzzle for it :)

no thanks