It would seemingly make sense for you to be able to give unbound items from one of your characters to another, but I don't know if there's a way to do this. Is there? I was thinking it might be possible through the Galactic Market but then I'm not sure if it's possible to sell to yourself or cancel a listing (and get the item) from a different character.
Yes, as long as they are on same server you can mail anything that is not bound to you to an alt. So any BoE (Bind on equip) or BoL (Bind on Legacy) item can be mailed to an alt. (Additionally, this is the only way to do cross-faction mail. If you want to send something to an Imp from your Pub, you'll need to funnel it through your Imp alt or their Pub alt first.)