Q:
Are gem items account bound?
All gem store items are account-bound on purchase, yes.
You’d still need to put them in the bank to transfer them between characters, though. There’s no character-to-character mail system or anything (that is, mail between your own characters). The bank is the one thing you can use to move items from one character to another on the same account.
The only way to give a gem store item to someone else (other than giving them a gem card code to get their own gems) is to use the gift option.
Account bound by definition means any alt can use it (do the bank transfer method, or just log in on the preferred alt before taking the item out of the mail). Some things will become soulbound when equipped, so check the tooltip for that. Once it’s soulbound, it’s locked to that specific alt.