Do you have it set up using POP3 or IMAP?
Based on your comment about folders, it's POP3.
Well, POP3 does not provide access to folders. IMAP does.
To use IMAP, you'll need to add the account into Aqua again, in Manual account setup mode, and enter server settings from the message just above:
http://www.aqua-mail.com/forum/index.php?topic=1577.0For the delete thing -- since POP3 does not provide access to server folders, if you'd been using "move to deleted" (which is the default), then messages on the server were staying in the Inbox (the only thing that POP3 provides access to).
In other words, the Deleted folder, for POP3, exists only on the device - and messages moved there in Aqua will continue to "live" on the server.
To purge the Deleted, causing those messages to be deleted from the server, please long press the folder and choose "Delete all".
You can set the app to do this every time you close it with the Back key -- this is in app settings under "Mail, other".