Automatic firmware updates are run as part of the build process initiated from the Visual Studio extension for nanoFramework. Please see the following blogpost: https://www.nanoframework.net/automatic-firmware-updates/
Currently all STM32 targets for both officially supported reference targets and community targets found in our nf-Community-Targets repo.
Not at this time. Currently this feature relies on the Cloudsmith API together with our repositories there, where we publish firmware packages. Supporting custom repos would require a standard way to access the packages storage and version querying. If you would like your board to be supported out of the box, feel free to add a PR to .NET nanoFramework nf-Community-Targets repo.
If you are running the build locally, the best approach would be to use the BUILD_VERSION property and sets it to a value which makes it "impossible" to find a better version e.g. 99.999.0.0.