I need to now if VS Code can coexist with Visual Studio 2013 and VS 2010 in the same Machine. (Work one) Sorry about this question, but I don't have much time for reinstalling everything if that fails.
VS Code is very lightweight and cross platform IDE ( for Mac, Windows and Linux). It could be installed side-by-side with Visual Studio 2013 and Visual Studio 2010. You could even install C# plugin with the Visual Studio Code and it would not interfere with Visual Studio 2013/2010.
If you want to be extra careful please make a restore point (in Windows) prior to installing VS Code. If something goes wrong you could revert to that restore point preserving your Visual Studio 2013/2010 installation.