All the message in Inbox are messages that should be in Trash?
Or all messages that should be in Inbox are instead in Trash?
Do you use any other email apps? Say, Outlook for Windows, Thunderbird, InnoMail, etc?
If you do - I'd guess that app must be set up to use POP3 and is also set up to delete all messages from the mail server after it checks mail. Can you check?
Mixing POP3 and IMAP is not a good idea.
You could switch your other email app from POP3 to IMAP.
Or you could remove the account from Aqua Mail (long press on it - choose Remove account from popup) and then add back, making sure to use the Manual button after entering your email and password and changing IMAP to POP3 on the next screen.
That's all I can guess from what you wrote.