Dos-box cannot launch programs that do not run in DOS mode, which I guess is what the batch files do in this case.

Put simply: no, this won't run in a system that cannot run .bat files. Wine, however, can run exe and bat (IIRC), but it can't run .NET programs. Still, I don't think you'll be able to put Mono and Wine together (Wine to run batch files and Mono to execute the .NET code)

If you really want this program on Linux, port it on a Qt GUI

You can install the .net run time in wine, either the MS implementation or Mono. But really he could/should just run the commands in the batch file directly rather than calling the batch file.

In fact running the batch file from the GUI is the wrong way to do it as the batch files are only there for convenience of people not familiar with the command prompt or other shells.

In any case having a configurable make command and clean command would be the best way to go, in place of running the make.bat and clean.bat.

Could not download the latest version of .net framework, will anyone please help me out ..

will you please tell me from which source did you downloaded the same