Sigh. Alright, let's get some facts straight.
Yes, Sakura learned Ansatsuken from just watching videos of Ryu fight. She's a fucking genius when it comes to martial arts, almost as though she had photographic reflexes. However, her techniques are very unpolished and untrained. Which is why they are inferior to actual Ansatsuken techniques. Her hadouken, for example, is a joke. It just looks big but it's not that powerful.
Dan did not teach Sakura. In an effort to find a strong teacher, she and Dan ran into each other. Dan offered to teach her if she could land a single hit on him. She...kicked as ass and decided that he wasn't really that strong to begin with and went on looking until she found Ryu. Dan, impressed by Sakura's skill, claims her as his student and makes repeated attempts to get her to join his Saikyo-ryu dojo. The reason Dan has techniques similar to Ken/Ryu is because he was also part of the Ansatsuken dojo as a student senior to Ken/Ryu. However, Gouken kicked him out because he sensed Dan's anger and rage and didn't want to teach him anymore for fear of Dan becoming evil like Gouki(Akuma). Reason Dan was angry was because Sagat killed his father.