Well, you could make Forge mods. My assumption is that they include some sort of Forge API. Meaning the SpongeAPI wouldn’t be available. I’m not sure how Visual Studio handles artifact dependencies, maven, gradle, etc.
You could make a Sponge mod in Notepad++. The question is, is the environment suitable for it? As far as out-of-the-box support, you’re not going to get that with VSF. But it’s possible, of course.
You probably could if you messed around with it. I would suggest using IntelliJ over it, however. You can find most of the information in the docs.
That is kind of true. VS is more suited to work with .NET Platform rather than JDK. I prefer VS over any IDE so I was looking forward making Sponge mods inside VS.
Well, you can. Nothing stopping you.
I just don’t know how to get started by creating a Sponge Template in VS that I can reuse on all of my Sponge Mods.
Well, you’re the VS expert. 
I don’t think you’ll find very many people here who know much about it.
I will try making a Sponge template on VS and If I manage to do that, I will definitely share it here. So far, writing Forge Mods in VS is much more convenient and simple than If I had to use IntelliJ(which I use for anything Java related).
I know a good deal about visual studio as I do a fair amount of C++ and C# development from within it. I have not on the other hand dealt with Microsoft’s new extension. From my experience it should be possible to create a template that loads up the JDK, a new maven / gradle project (whichever suits your preference, just make sure you have the plugin / extension for it) and has the SpongeAPI as a dependency. It would also need to be configured to be built to a jar file. Running it from the play button in visual studio might be possible with a little fancy run configuration work to copy the output jar into the plugins folder and launch the server (no clue if remote debugging is possible).
Awesome. Would you mind sharing if you figure out a way? I have no idea how extension works in VS.