For the record, I managed to solve my Thunderbird SSL/TLS problems by keeping protocol filtering enabled, but adding the IP address of the IMAP server (a local address on my home network) to the Excluded IP addresses list, found in Advanced setup > Web and email > Protocol filtering > Excluded IP addresses. Maybe not the correct or best way to solve it, for for now, I'm good.
I presume my firefox errors were a result of certificate regeneration, which I handled by following the advice above.
itman, I connected my computer using Ethernet cable before doing an update, and this time the network remained up. I should test it one more update before I can say it works, but it looks like it does. What does that tell us?
Btw, as I mentioned, I am running Windows 7, not 10.
EDIT: And I now just did a second update with Ethernet cable, and there was no network failure. I also noticed that the little icon in the system tray did spin for almost exactly three minutes after updating, similar to the time that the wifi is down. Is that a lead?