Short answer: Yes. More detailed answer: Syncthing just needs a network connection in it’s original definition. A network connection doesn’t imply internet connection, just some network that is TCP/IP capable is enough. You do not even need a router, connecting two computers via Ethernet cable (or even WiFi direct and similar) would work too (altough it may require some amount of configuration).
Syncthing traffic is encrypted and authenticated, what exactly is it you’re worried about?
Yes, that’s possible. Again, any type of IP network will work. Depending on the exact network setup it will either require some configuration (for example static IPs in the computers or address configuration in syncthing), or it may even work out of the box.
You can tunnel pretty much everything over USB, wouldn’t be surprised if software exists that can do IP networking via USB. This may require third party software though, it’s not a feature syncthing has inbuild. In general it’s not something that I would suggest as the go-to solution, if it even exists.