The frog will deliver all your auction purchases to you unless it has trouble getting to you. (Like if you log out, reload, possibly in some instances.)
There are no mailboxes in Ilmenskie Deeps or the Caverns. The closest is in Uralia. (Mailbox in Oktyabrya, Dispatcher in Eastern Approach) Or Guillermo Gamera Way, Ix (Mailbox and Dispatcher)