Multidimensional Scaling with Categorical Data
MDS only requires a distance matrix which stores the distance between each pair of data examples. How to compute that distance depends on the kind of data you are dealing with. If you only have numerical (real valued) features, you can use the Euclidean distance, but that is not always the case. 

For instance, if you have both numerical and categorical variables, you may apply any metric for mixed data, like for instance this one. 

Regarding your second question, I need further clarification. What do you mean by "converging? Are you asking if both algorithms converge to the same solution? Is that is your question, the answer is no, because the aim of both algorithms is different. MDS projects your data onto a 2D plane by trying to keep relative distances, whether PCA projects data by focusing on those "directions" in which there is more variability.