How Do I re-install Mail?

My patience has finally run out with trying to tweak my mail to work properly.
It's connecting to my online pop3 mailboxes but the mail is not downloading onto my Mac -90% of the time, that is - (the mail then gets marked as read in my online mailboxes - there is the proof it is actually connecting to the mailboxes).

So How Do I Do A Complete Re-install of Mail? What do I have to back-up, etc.

And I thought, after my move from Windows, these sort of problems would be over. Sheeesh!!

It is probably not necessary to reinstall Mail. Reinstalling things is more of a Windows "repair" method.
If you are connecting to the mail server, but it isn't downloading the mail, it could be a number of things. What mail provider are you using? It could be a problem with your ISP or your email provider.
You could also trash your Mail prefs and delete your user account from Mail and set it up again. Repairing permissions may help as well.

Repairing permissions. Could you explain.

I'm logging onto yahoo.de and web.de pop3 mails. Until a few days ago the web.de worked 100% ok. The Yahoo has been a bit 'iffy' for months. (The yahoo.de accounts work differently to the yahoo.com accounts, they are accessable from any computer).
If I wipe my accounts and re-setup, what do I have to do to protect my mail I have?
My ISP is MaroccoTelekom.