It's a small one, but one of the main themes in the movie is the importance of brothers and brotherhood. In the original Prince of Persia game, Jordan Mechner (who helped write the film) used photos of his own brother to create the Prince's sprite. Jordan's brother brought the Prince to life. Neat, huh?
Related to the lack of sand zombies: If Dastan could extract their Sands of Time, he'd probably just abuse the Dagger of Time at every pivotal plot point. Perhaps that's why they weren't in the movie?
Nizam displayed surprisingly competent swordwork immediately following his Villainous Breakdown, the reason he was such a pushover during the film's climax was because his hands had been burnt in that timeline.