Yes, though it’s not limited to two parties. You can form clusters potentially spanning dozens of devices (your hardware is the limit).
Not really like a cloud service, because those use central (always online) servers to store your data. So any device can download from those servers. Syncthing on the other hand is decentralized with equal devices - there is no central storage (unless you host one yourself). So you must have at least two devices online at the same time, to allow sync. Data is only stored on devices you have installed syncthing on, no third parties.
But yes, it runs in the background and updates files on other devices, when they are changed somewhere.
No, syncthing doesn’t use Git in any way (well, except for it’s source code on Github, but that’s unrelated to the application itself). The protocol used internally is custom (and documented here, though that is highly technical and not for users to understand)
Syncthing operates in folders. Those can be added via the web ui and represent actual folders on the filesystem. Folders can be added in any place (where the application has read-write access) and it can also use pre-existing folders anywhere on the filesystem. Everything (except for ignored files) inside these folders is synchronized. Over the UI you can select devices and folders to synchronize.