Is there a way to get the mex file for a built-in MATLAB m- file? If yes, how? If no, does that mean I have to write the C code myself (oh nooo!!!)
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The Matlab built-in functions are closed-source. Thus, you won’t be able to get the code for them. It is possible to call Matlab functions from C code, though, if that solves your problem.
Depending on the function you want, you can find some of it elsewhere. For example, linear algebra operations are in LAPACK, and you may be able to get something from the source of OCTAVE.