Just a blind shoot in the dark: I do not have access to AutoCAD2013.
I do not think it has anything to do with .NET version, nor VS version (2010 vs 2010), because you are doing a standalone exe to automate AutoCAD. The .NET version of your EXE app has nothing to do with AutoCAD. You can do your app with .NET2.0, 3.x, 4.0 or 4.5. And certainly you should not bother to change <startup.<supportedRuntime.../></startup> in acad.exe.config, just because you want to automate AutoCAD froom external app.
Yes, it is very likely the 32-bit and 64-bit issue, but not because of Win7, I'd guess.
One possible thing to look into:
Since Acad2013, I have heard, Autodesk stops install AutoCAD interop assemlies (PIA, which wrapps AutoCAD COM interfaces that you use for automation) into GAC. With pre-2013 AutoCAD, you added rerferences to AutoCAD COM, but VS does not generate Autodesk.AutoCAD.Interop.dll, beccause it already exists in the GAC. But with Acad2013, I guess, VS has to generate the interop assembly (with tlbimp.exe tool), or you make sure you set reference to the interop assebly from the downloaded ARX SDK and the assembly has to be either copy to local or to be embeded.
Since there are 2 sets of interop assemblies from the SDK for 32-bit and 64-bit AutoCAD, I not very sure which one you should use, but I'd try the 64-bit version one: although it doe not matter what your exe app builds against in term of CPU (Any/32/64) when it automate AutoCAD, but since it has to communicate with AutoCAD via the interop assemblies...thus, try the 64-bit interop assemblies first.
Again, since I do not have access to Acad2013, so, just some guesses that may be of a bit help.