Yes, mojoPortal can be used with MVC. We're currently running Visual Studio 2017 but you should be able to get away with using 2015. I suggest you get the code from the repository though, don't try to build against the released files using Visual Studio. That'll probably cause you more headaches than it's worth.
Follow the advice in this article for connecting to your other database. The advice there references MSSQL but the same logic can be followed for PGSQL. I suggest writing your code (Views, Controllers, etc...) in a separate project. Easiest way to do this is to download the repo, open the solution and then create a new project and add your code there. When you are ready to publish your feature, you can use Visual Studio's publish feature to put the code in a separate folder on your computer. You can then copy your published feature to your mojoPortal site and run setup (/setup/default.aspx).
Be sure to check out our Developer documentation.