The Submit tab is for inputting anything that requires correspondence.
Claims are an open forum for you to submit things to the staff. For example, You can submit any artwork that you created for an award of additional coal. Claims are detailed on this page here [link required].
The Design Approvals page allows you to review any design updates you've put through the system. Unlike other Lorekeeper systems, Beelzebubbies does not use the MYO (make your own) system integrated in the site. If you would like yo use an MYO, you must instead submit a claim. More about this is detailed in the design guide.
The Character Transfers page details all your pending character transfers, similar to the design approval page. To transfer a character to another user, go to that character's specific page.
The Trades page is specifically for trading items between users. You can use this to send gifts to friends, trade items for art, or even items for designs.