No, once a campaign's window closes, there's no way to earn its rewards by watching, live or recorded. The items are only obtainable from someone who already claimed them during the original campaign.

Yes, a Twitch account has to be linked to the relevant game account before any watch time counts toward a reward, this is a one-time setup that applies to future campaigns too.

Yes, items from a purchased Twitch Drops campaign are kept exactly as shown in the listing.