Is multiprocessing possible on a Turing Machine?
This is a subtle question.

TMs are very much a sequential model of computation. So in some sense, TMs cannot (directly) model multiprocessing. However, TMs can do step-by-step simulations of the reductions a multiprocessor is carrying out. So TMs can do a sequential simulation of a parallel computation. Whether this a genuine model of parallel computation is debatable.

See also the discussion Applicability of Church-Turing thesis to interactive models of computation.