Stupid Question, but...

you already answered it yourself :D

Nope. Only steam redeemable games can be used to mage a giveaway, if it's for origin you can either just drop the code on the forums or maybe try galagiveaways, I think you can give Origin games there.

Nope, Steam gifts only. You can create a special puzzle or something with the key in the end, without forgetting to say that it's an Origin key.
Or you can simply drop it in the chat or the forum. :)