How were Medieval Cavalries taught and trained to fight? What places are needed to learn horseback riding and cavalry tactics and do also you need to be a son of a Noble/Knight or at least be there vassal to become one?

Eh, the question of training is a difficult one for the Middle Ages. If anyone would like to chip in their own knowledge on the topic, please don't let this post stop you! For the meantime, OP, we can bring forth the Medieval Armies Compilation to get some answers:

u/Rittermeister explains the difficulty in answering the question of training;
u/PartyMoses observes that the notion of 'training' isn't quite there;
and u/TheGreenReaper7 has input from a French knight of the 1300s on the matter.