The answer to your first question is: yes, you can. What I do ask is that whatever rank they have in the PPDC reflect the way that professionals are generally ranked in the current, modern Earth context. AKA, we don't have a nurse as head of medical, as that's not the level of expertise required to be head of medical, and so forth. Match up what level of education and experience your character would need in a "real-world" context, and yes, being at a high level in the PPDC is fine!

Mute characters can become pilots, and presumably will be taught a form of sign language if they don't already know one. They'll be expected to write in English and whatever is their native language, and the PPDC may even be able to bring in a sign language instructor should other students or PPDC staff want to pick up sign language as well.

Characters are not mute in their own minds, since it's not language but memory and sound and all sorts of emotions and thought impressions and such in the Drift, so it would have no effect on their technical ability as a pilot.