Ah, so when you wrote that "the junk folder shows 0 entries even though it contains new unread messages" -- you meant "0 in AquaMail, actual messages in web mail"?
Can you make sure that the Junk folder is set to sync in AquaMail? Long press the account, choose Options and Folders -> Folders, tap Junk mail (or whatever it's called by Hotmail, I forget) and choose "Sync as spam". Then back out to the account list and refresh this account.
If this doesn't help, please do this:
Long press the account, choose last item ("Diag: message dates"), choose Junk mail, and run the test to completion. At the end, you'll be prompted to send me a debug log.