The events in Kingdom of the Sun happened before Emporer's New GrooveSo hear me out, in his youth, Pacha looked a like like Kuzco's dead dad, Manco. Yzma was somewhat younger and still vain, and the pretty boy lackey was the previous model before Kronk. Yzma's father being the Grand Mortician allowed her to stay alive much longer than she other wise should have, and some act of heroic forgiveness on Manco's part forgave Yzma of her crimes, an action he would not live to regret. Manco died and Yzma ruled in his stead, raising Kuzco.
Kuzco is left handed.The arm he has to use later is his left. He also does the kiss stamping thing with his left.
Yzma isn't evil.Think about it. She tries to kill a greedy, selfish emperor in order to seize the throne. She buries this with a lie in order to preserve her own safety. She did "practically raise" the man and he constantly insulted her and fired her in a cruel way. Her compassion and empathy is shown when Kronk fails his task, putting her life severely at risk, and instead of killing him as most villains would, she gets him to help her find the enemy. She never seems to consider killing Kronk despite the constant times he fails. And as for putting Pacha's life in danger, well he was helping said emperor and being a risk to her freedom and possibly her life. And then there's the matter of "and why do you think i should provide your family with food?"... would Kuzko have been any more generous before his redemption?
Yzma is immortal.That's what some of her potions are used for, and indeed, likely the reason she started making potions to begin with.
Pacha's kids are psychic.They dream about his rescue of Kuzco, so it could be some form of clairvoyance or possibly a weak telepathic connection to people they're closely related to.
Kuzko will become the greatest king in his people's history.He'll use the potions from Yzma's lab to make super soldiers and make a massive empire, naming the new capital after himself. Unfortanitly as time goes on records of king Kuzko will disappear and all that will be left will be his city.