I presume this is an IMAP account, - click to account settings pane - click the synchronization&storage pane and then the 'advanced' button to verify that the desired folders can be downloaded - now, click File>offline>download from main menu - (if menu bar not showh, click the Alt key first) - this should dowload all messages - now, install the importexporttools NG addon - highlight each folder in the account, rightclick and select the importexport option to export messsages in whatever format you wish. - although not needed, I also suggest then highlighting Local Folders, rightclick and then use the importexport menu option to import from the exported media. That assures you that you have a good copy of the messages. - you can now close out the account.

And, just to clarify, Thunderbird does not have your data and never did; it's only an agent.

Oops, I forgot the second question. If this is a current version of thunderbird, click the account settings pane, and on right side of the account pane is a Delete button.