The templates not showing up during install seems to be a quirk of Monogame 3.5 and affects all versions of Visual Studio. You will need to install Monogame then place the templates in the correct folder manually. Check out this thread:
The templates are found in the dropbox link. Unzip the download then put the entire folder here:
c:\Users\YourName\Documents\Visual Studio 2010\Templates\ProjectTemplates\Visual C#\
This should get Monogame project templates working.
All of this said, I’m not entirely sure if 2010 is supported (despite what is listed on the downloads page). I can load up and work on a Monogame project just fine, but if I ever close and reopen the project in Visual Studio, I get an error message that “this version of Visual Studio is not supported.” I’m curious if you get the same message or if there is a workaround.