origin

No, I'm sorry, but that's against the rules.

on the forums yes, but not on a giveaway

No

You can post them in the forum, but you can't create giveaways. Winners are required to activate their wins in Steam or get hit with the ban hammer. Winning an Origin game means not activating in Steam, and only causes problems.

No, but you can drop them in a forum post so people "ninja" them.

There were exceptions but not anymore.

Also, you will want to delete your Sims 3 giveaway, the Origin bundle did not include a Steam key for that game. The given keys are for The Sims 3 website, and only activate the game within your Origin account which is linked to that site.