AquaMail tries to map those "special" folders based on their names and also based on the IMAP "XLIST" extension. Guess it's running into trouble with both.
"other mail apps" --> can't speak for all of them, but e.g. K9 (based on an old snapshot of stock Android Email) will *create* folders using English names like Drafts and Sent and Deleted on the server if it thinks it has to. Not sure if it's the best solution.
Back to AquaMail:
1 - Please use web mail and make sure that your account does have Drafts / Sent / Deleted folders (just in case) and that they're accessible over IMAP (this part is mail provider specific, for example Gmail lets you turn IMAP access on and off, per folder)
2 - In AquaMail, long press the account -> options and folders -> folders
- Let it refresh
- Find the server side Deleted folder, tap its name, choose "Sync with Deleted"
- Same with Drafts and Sent
- Back out to the main screen, which should now have those "special" folders visible