Margaret, i have a few email accounts and a hotmail one, my Bt and hotmail ones
i have emails in those going back to 2007, and during that time have changed machines and formatted etc
and never lost them, like you i have various folders and in my bt one i can multiple select mails and move, forwarding yes you would probably have to do one at a time.
i did have a GM mail and just checked as i havn't used it since nov' last year and all mails were still there,
but not sure how their archive works as i only used it as a backup,
same as hotmail i wouldn't rely on it for important stuff, if you don't sign in for a period i THINK you may lose some,
but like anything if important backup

or after all my prattling lol as Marky says you can try gmail backup