I haven’t used BTSync in a long time, but it’s pretty reliable.
Yes
Yes. There’s no concept of a “free tier” or anything - Syncthing doesn’t take money from its users (other than donations). Obviously there are limitations: the largest known cluster has 104 devices, and that’s probably running on some pretty beefy hardware.
It isn’t based on the same Bittorrent protocol as BTSync: it uses its own protocol (called BEP). BEP is peer-to-peer in a similar way to Bittorrent, so it will send and retrieve data from multiple devices.
Yes. If you disable Global Discovery and Relaying then Syncthing won’t attempt to connect to anything over the internet (or be connectable to anything from the internet).
Take a look at the community-contributed wrappers if you want a slightly nicer user experience. SyncTrayzor (for Windows) and Syncthing-GTK (cross-platform) in particular make the user experience quite a bit nicer. You’ll also find the Android client there (or in the Play Store or FDroid).
Is there a better android client for syncthing? The one I downloaded from FDroid is not that pretty. It was hard work adding a folder on Android. I did several trial and error and finally I was able to sync. Is there a tutorial on how to use this thing on Android?