The Debian package has been available officially from 3.7.19 - unofficially from 3.7.17. Unfortunately it wasn’t advertised through the regular download page - hopefully that will change when 3.7.21 is fully released.
The regular Vassal upgrade notification will be shown when a new release is available.
Note, however, that the Vassal package isn’t in Debian proper, so you won’t get the package from the official Mint repository - you still will need to download it from the Vassal download page. Hopefully, we will get Debian to accept Vassal into the official release.
Correct. You simply download the .deb and install that (by double-clicking it, or using sudo apt install ./vassal-<version>-1.deb).
Yours,
Christian