My F5 has a corrupt boot partition and wont boot. How can I switch boot partitions?

You can try to boot from USB to recover it. See https://support.f5.com/kb/en-us/solutions/public/13000/100/sol13117.html

Upgrade instructions are usually in the release notes for the release you are upgrading to. I just did 10.2.4 to 11.2.1 and don't recall anything special needing to be done. I usually run it through iHealth first to make sure nothing comes up that could prevent the upgrade, as well as re-activate the license. I've never seen an upgrade stop it from booting, usually it just comes up with no config on it because the upgrade script couldn't complete.