woah, u know some thingis.
Ur first paragraph is true. He was a "doctor" but with a lot of warfare affairs.
He indeed occupied those charges u mentiones, but in fact he failed in all of them because of his lack of knowledge in the subjects. He was even in charge of some ministry of peasants of something like that, in which he failed too.
In the end he was sent to Bolivia by Fidel himself, as the later didnt wanted top share more protagonism with him in the movie, so it was better to send the crazy Che to an impossible task.
But taking out his military issues and the lot of people he killed , Che was a cool guy