Can I keep my trade between packs?

To address points 1 and 3, once you've earned a trade, it's yours to keep. Your character can become a lone wolf or join another pack and not lose a trade they've already earned, though the new pack may ask them to prove their skill before they acknowledge your character's earned trade.

Point 2 is probably up to a pack's leaders. It wouldn't make much sense for a character to earn the spy trade in pack B if they've never spied for pack B, for example. Some leaders may take your character's word for it and accept retroactive threads, others may not. If you change packs in the middle of earning a trade, there's a possibility you'll end up having to redo a few trade threads in the new pack to demonstrate to those leaders what your character can do.