Frederick did receive an education of sorts, but i would say he didn't really begin it until after he was released from prison and slowly worked his way back into his father's favor.(a sad story really) imo napoleon received a better education in the military arts. It wasn't really until a few years before he became king that Frederick began to take it seriously.
Tho his education did provide a lot in terms how to handle the civil side of his kingdom.(something frederick did a lot with)
as for generals or promotion though the ranks. Yea, frederick didn't really trust non nobles. He was somewhat forced to during the 7 years war to allow non nobles higher in the ranks, but not too long after the war he removed them from their positions. I want to say that he believed that Nobles had honor to uphold and if they didn't behave properly, they would lose any honor they had, dishonor their family name, and more or less be shunned by the family. by contrast, non nobles would go back home and pick up where they left off in whatever occupation they had prior(blacksmith, farmer, etc.,) he did reward good deeds and punish cowardice or otherwise incompetence by his soldiers and officers.(sometimes in a funny manner)
Frederick for his time was pretty progressive in his thoughts and actions but he still had prejudices.
I would say in at least a small part, the French revolution occurred thanks to frederick. With the diplomatic revolution(his actions helped influence this happening) where the french and austrians allied, the french and austrians sealed it by a marriage. (maria Antoinette and Louis 16 ) So napoleon can thank frederick for setting up the french revolution
(this last sentence is just a joke)