.NET Framework 4, 'Unhandled exception has occurred in your applicatio

I'm guessing the program is still being developed since it's an Alpha version of the program, therefore there is most probably many bugs which need to be fixed.

From the error message in your first post, it seems that an error (exception) occurred in the routine within the actual code of the program itself, and the developer hasn't added a alternative handling routine, to enable the program to respond to the error and therefore not crash completely.

I would go to the support or blog page where you downloaded the mod, and then report your findings, they may then add a patch for the bug.

The error has nothing to do with the .NET Framework, but instead is a clear signal that the program itself (the mod launcher) has a bug that created such an error.

From the stacktrace you posted, it shows that after you clicked the button, it tries to start another program (the game, I guess) but it doesn't finds it, hence errors out. Is the game or the mod itself properly installed? Maybe a reinstall of those help.