Yeah, you don't need a VPN as their is also a relay component that forms a sorta sync thing network. While the data is always encrypted, with the relaying you are using external servers to route the traffic. The relaying also isn't required, but ensures data can be synced even when a direct connection isn't possible (e.g. You arent home and aren't on your VPN).

Yes, you can sync between two on devices anywhere in the world as long as a connection path can be found.

The downside of this is that both devices have to be on. If not on the LAN it may go though some unknown gateways too which makes me nervous (though it should be all encrypted). It can take some time too for the devices to find each other and then do the transfer (even on the LAN).

Some people place syncthing on their NAS so it is the always on device. Also if you do not want your connection to go through other peoples bridges then you can disable that feature (and loose the global WAN transfer capability), or you can put up your own bridge in a VPS on the WAN.

I am no expert on this. For me I use syncthing only sometimes and only on my LAN. Mostly I use SSH, Nextcloud, or Bitwarden Send myself. I'd like to play more with some of the other options though. Seafile or placing Send on my VPS for example seems interesting to me.