How can I prevent anyone from deleting mail in my box?

One way is to allow everyone else to have their own login and not assign them as admin accounts. Then change your iMac login password AND your email password, so nobody can login as you or view your email.

7575P wrote:

Difficult to change e-mail since everyone knows me by the one I have.

Don't change the email address, just change the password to the email account.