Visual Micro is a free plugin for MS Visual Studio that supports Arduino 3rd party build processes. However, according to a post from March it’s no longer compatible with Arduino. Still I would suggest you to try with this plugin and see if it no longer works, check this link Microsoft Visual Studio IDE for the Galileo and Edison.
About debugging an application from Visual Studio, we have no experience with this. Maybe you can find some useful information from here http://visualgdb.com/tutorials/linux/edison/. I would also suggest you to contact the Visual Studio support team, https://www.visualstudio.com/en-us/support/support-overview-vs.aspx.
1. Visual GDB - cool pulgin, but for C++ developing. Maybe it supports C#. Requested technical support
2. Visual Micro - Arduino way.
3. Visual Studio support team - Ask them on the forum
Also found another solution MonoDebugger.NET - Debug your Mono applications with Microsoft Visual Studio
The project looks not alive, but maybe can be modified. The source code is on github.
If I find a solution, I'll write in this thread
P.S. Answer from support Visual GDB: "Visual GDB not supported C#"