If you play in a official tournament where proxying is forbidden, are you allowed to use promo cards instead of normal cards? E.g. you have no Tantive IV, but have the C-3PO promo card. Can you use it?

I'm no TO but I don't think the alternate art cards count as proxying cards? They a reward for taking part in the organised play community. I'd be gutted if I couldn't use my hard won alternate art cards (all of the one I have, not really won as it was the door prize...) in tournaments and other official events.

If they're official FFG cards then they're legal. They can be alt art, they can be in a different language, ect.. as long as they're official FFG cards then they're legal.

The promo cards you speak of come from ffg tornament kits purchased by hobby stores.

They are just as legal as ship bundled upgrades