My question regarding the running speed of skeletons and zombies, can they run as fast as an unencumbered character or are there limits?
For constructs, (unintelligent), how fast can they run? Is their speed dependent on type, (clay, flesh, iron, stone)? Some of their descriptions state an ungainly gate, would that preclude running as fast as a PC?
Each of these creatures has a speed included in its statblock. There's nothing in their rules or stats preventing them from increasing that proportionally via the run or charge actions, with the exception of the zombie's limited action clause. And there are zombie variants that don't have that.
Generally, faster than the party's halfling.
Unless a monsters statblock says differently, monsters work the same as PCs do. So a monster (regardless of type) can take a full-round action to run 4x its base speed (or 5x if it has the Run feat).