How to play a character with a disability or mental disorder without being offensive?

Two character concepts I’ve had recently are as follows.

  1. Someone who has been permanently deafened by their master as a symbol of their subservience. (NPC)

  2. Someone who has had a significantly traumatic experience, and as a result, has PTSD. (PC with the haunted one background)

Both of these concepts require a nuanced approach. For example, I recognize that concept 1 would have trouble communicating verbally, and I don’t want to play this character with an off-the-cuff Hellen Keller impression.

How can I explore these and other character concepts in a way that would not be offensive to any affected parties?