Is resharing instagram still possible?

Goes the other way too. If you want people to be able to reshare your posts (or stop them), there's a sharing section in your own settings that controls it.

Yes, mostly. Tap the paper plane under a post and "Add to story" puts it on your story with a tap-through back to the original. There's also a repost option on a lot of posts and reels now, which drops it into a reposts tab on your profile instead of the story. If neither shows up for a particular post, the person who posted it has turned resharing off, or their account is private. Nothing you can change on your side for that one.