Re: long story about Trash folder
Yep, creating the folder yourself is what was suggested a few messages up.
You didn't have to use Samsung's mail app for it, it would have worked from AquaMail or web mail too (but you probably thought that Samsung's app would magically find something which said was not there... and it did not...)
Re: they all stay strikethrought
Long press the account in AquaMail -> options and folders -> IMAP options -> make sure to enable "EXPUNGE"
It is enabled by default, I'm guessing you might have turned it off while experimenting.