Is Parks-Mcclellan algorithm guaranteed to stop?
You have to distinguish between the algorithm and a specific implementation. The Parks McClellan algorithm is based on the Remez exchange algorithm, which is guaranteed to converge. So in principle any correct implementation of the algorithm should converge. However, convergence of the algorithm is only guaranteed if all intermediate results are computed with infinite precision, which is not the case in a practical implementation. Some design specifications can result in numerically ill-conditioned problems that will prevent correct convergence of the algorithm.

In short, yes, the algorithm is guaranteed to converge. However, in some cases, numerical problems can prevent convergence to the optimal solution. But even in the usual case  of convergence, the number of necessary iterations cannot be determined beforehand.