I don't think mingw and msys work well on WoW all together, at least in my experience, the 32 stuff has to be run on a 32 but OS, and vice versa for 64 bit.
No, that's the whole point of WoW: you can run Win32 executables on Win64. Running the Win32 cross compiler on Win64 works fairly well, I was told (by Fortran users; I don't know about g++).
For your issue, you should try running the compiler with its full path: "C:\foo\bar\bin\g++.exe myfile.cpp". It helps the buggy GCC driver.