Sands of Time Prince's Generic Rage persona was the Dahaka's faultNot just because being forced to run for years, no one believing him, jaded him up. The Dahaka was also able to directly corrupt him somehow, and do it very thoroughly. Maybe it's not the only one of its kind, and reproduces through converting the people it chases. Being exposed to the Sands made the Dahaka in him sort of separate from what was left of the rest of him, resulting in the Dark Prince, a combination of Dahaka and sand monster.
The Prince already made a Deal with the DevilThe 2006 Prince, that is. That's why he can grab ledges after falling a distance without ripping his arms out, and why his sword can effect Ahriman's soldiers, which appear to be nothing more than wind and darkness. It also explains why the Alchemist's gambit of infecting him with the Corruption didn't work — his soul was already promised to another demon, and so Ahriman couldn't take it.
All of the Princes are related.It's very possible that the original Prince could be the father of the Sands of Time Prince, while the New Prince could be a distant cousin.
If Sand Monsters are near the Dagger of Time, they are immortal.In the Sands of Time when a Sand Monster is killed, it revives unless it's sand is absorbed. When the Prince loses the dagger, the monsters stay dead when killed instead of being revived. In Warrior Within the Prince doesn't have the Dagger and the monsters die when you kill them. Clearly, this means being near the Dagger gives them a bizzare immortallity.
Azad's justice system was run on the same lines as that of Dwarf FortressThat's why so many of the enemies there wield hammers. They weren't prisoners, they were executioners.
We've been going backwards through the seriesThe 2008 Prince is the first one, he marries Elika and they have a child, the child is either the Sands of Time Prince or his father. Then The SOT Prince has a son, the Classic Prince.
The games take place in the Assassin's Creed universeThe Ubisoft games, at least. The 2008 game takes place thousands of years ago. Ahriman and Ormazd are two of "Those who came before", and Elika and the Prince have quite a lot of TWCB blood in their veins, and the much later Sands of Time Prince is of the same bloodline. The Empress of Time is either one of TWCB, or a powerful weapon invented by them. Same goes for the Dahaka. The hourglass, medallion and the dagger are all TWCB artifacts and the human bad guys are all Templars.
Malik from Forgotten Sands is The Mourning KingBoth of them look pretty similar, and wear similar clothes/armour. All we see of Malik at the end of Forgotten Sands is him collapsing. He went into some sort of coma, and when he woke up, didn't tell his family that he was still alive out of shame and embarrassment at his possession. He fled to another kingdom, eventually became its ruler, and this led to the events of the 2008 Prince of Persia game.
The Dahaka is a sand monsterIt can't pass through water, dies when it falls into the sea, and is clearly hurt by the Water Sword. Now, does a beast which represent fate itself sound like it would have those vulnerabilities? More likely, it's a sand monster impersonating the real Dahaka, of which there are only legends.
The trips to the fountain of life in the first game are really an early representation of the prince fighting the very onset of the darkness that would take the form of the dark prince two games laterThe game seems to make a point of giving you an easy to find fountain when you have Farah near the end of the first game, and she doesn't seem to notice you were gone. Not to mention that each hole leading to the fountain always disappear as if they never existed. Its really just a glimpse into the prince's soul and partaking of the water is a means of countering the corruption the sands bring onto him.