WE GOT CASH TRADE ROOM TEY ADDED IT HOLY pomegranate

You keep missing the point, it doesn't matter if it's permanent or not.
If you could trade it regardless of having used it, you would not need to buy extra pets for your other characters, you wouldn't need to buy one for both your aran evan and adventurer and what not, you'd only need one.
But whatever, let's end this discussion.

yes you do.
they aren't transferable through storage, only cash shop trading room.
you'd need each character on their own account.