How to prevent Mail from auto-deleting old emails?

As per this article : Mail for Mac: Mailbox Behaviors preferences in Mail

If you selected None for Trash Mailbox, you can choose to have Mail permanently delete messages automatically.

If your email account provider sets up the server to delete older messages, the messages are deleted regardless of how you set this option.

You can set as after one month ( click on drop down arrows options are there to choose ) .

Not knowing how you saved the messages on the computer with the POP settings, I suggest you create local mailboxes and copy the messages there to ensure you won't lose more. Or, make sure you have good backups.

It's to your preference on whether you want a POP account or IMAP. IMAP works best when you have more than one device in order to keep messages synced between both. Also, storing messages depends on how much space your provider allows. If you have limited space on the server, you will need to copy those messages to local mailboxes on one or both computers.

Can I flag select messages to be saved locally on IMAP accounts?

You would need to create rules to copy messages to local mailboxes.

Can I flag select messages on a POP account to be retained by the server?

Yes. In Mail preferences, you can set the server to never delete the messages.

Can I convert an account to/from IMAP to POP without deleting and recreating it?

You must at least disable the account before creating a new one. You can have 2 active accounts on the same computer to the same server with the same login & password.

I suggest just disable it (in Mail preferences) first before creating the new one. That way you can always go back to it and enable it if you choose not to use the new one. Once satisfied, you can delete the extra account.

Open mail from web browser and check the box for enable POP for all mail .