Soldato
So long as the Boff's and Doff's are not bound you can trade them. Your bank is PER CHARACTER, there is no account bank. The only bank that can be accessed by more than one toon is a Fleet Bank.
However if you mail yourself all the items, any toons on that account can pick up the mail's. Although if you do this, I would only bother mailing anything thats uncommon rarity or better.
Could I also send EC and Dilithium this way?
Also, can you mail the Boff's and Doff's? I assume this small issue with these would be that you have to be Lv5(right?) To use them, so I assume you would also need to be that level to receive them, and then trade them again?