That depends on the specific TLS setup. Badly configured TLS 1.2 would allow downgrade attacks, TLS 1.3 would not. I highly doubt the “in most circumstances” line, my guess would be that at least the big ones like gmail don’t allow unsecured communication with their servers at all. If not for their users’s privacy, then at least to combat spam.
No, they are not. They are not end-to-end encrypted but they are encrypted between your PC and your service provider, between service providers and between service providers and receivers. End-to-end encryption is needed to defend against your service provider or entities that can order your provider around but not against random hackers snooping around in your network.
Fax on the other hand is never encrypted and also not signed, so there is no integrity protection. Fax is far, far less secure than even standard email. Businesses require fax often for legal reasons because laws are written by people with no technical understanding not because of any technical reason.