How can I finally erase the mails, so they are gone?

It's called 'compacting folders'. https://support.mozilla.org/en-US/kb/compacting-folders

Are you using the Allmail folder? If so, you can unsubscribe by highlighting account on main view, rightclick, select subscribe and untick allmail. Thunderbird has no need for the folder and that should free up a lot of space for you. For more specifics, you should submit a screenshot that shows the folders and sizes, as it may also be that some folders are unintentionally duplicated.

Hi Christ1 Thx for your time. Cannot compact, bc there is not enough free space. That is the problem. Hi David Thx, I could not 100% follow your instruction, but I managed to tick that sent messages should not be kept in ALLMAIL, maybe that will help...

What was reason you couldn't follow it? And, Gmail controls allmail, so I'll be surprised if it honors that request. You can also go online and specify to not show allmail on imap.