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?

As with anything game related, I suggest first communicating your intention with the GM and other players and solicit their feedback. Don't just get feedback prior to the start of the game either. Check in after the first few sessions and be sure to leave the door open for feedback at any point in the future. Being open and responding to feedback honestly goes a long way if you were to make a faux pas.

Now, I don't believe a deaf character would require a different approach other than how you communicate with others. This should be decided prior to the start of the game. Does your character have the ability to communicate in another way, such as a form of sign language? What other characters can understand that sign language? Does your character write their thoughts down to communicate? What is the overall literacy rate in the GM's world? Communication is often hand-waved so, if your GM agrees, this may be a moot point.

For a character with PTSD I would suggest doing some research into PTSD and deciding how the symptoms manifest. I would also suggest making your thoughts on those symptoms known during your pre-game discussion with the others at the table and adjusting based on their feedback. There are a number of excellent resources available online but for a a cursory rundown of the disorder, the ADAA lists symptoms here.

I think the key thing to take away--and I'm not suggesting you aren't aware of this--is that people of different abilities or with different life experiences are people. Go into the game with a clear picture of what the character's hopes and motivations are and the rest will fall into place.

Do your best and recognize your mistakes.

By merely asking this question, you've acknowledged that you want to be as respectful as possible, and that, by extension, you're a compassionate person. As you're playing your character, keep that respect and compassion in mind, and you'll almost certainly be fine. Research, as TookyG's answer suggests, can only help.

And perhaps you'll screw up! Perhaps you will descend into stereotype because it's easier or accidentally make your PTSD-addled character as a sociopathic hobo with a shotgun until you realize "whoops, that's a really bad way to portray someone with mental issues." Fortunately, you're not making a movie for millions of filmgoers--you're putting on a performance for four-five other people at the table, one of which is on his phone and not paying attention. Improve the character if you can, resolve to do better next time, and move on.

In my current game, I realized far too late that I had constructed the role of Dragonborn in my society to be a rather blatant and insensitive racism metaphor. I even commented to my Dragonborn player, who agreed, that if I had meant the metaphor, his views and actions would undoubtedly make him the bad guy. So I have to chastise myself a bit, remember to not do a knee-jerk 'conquered indigenous population become slaves' background bit in future games, and do my best next time.

If your NPC was struck deaf after learning how to speak, they would not have a funny accent at all. But they would have trouble noticing when someone is talking, if they could not see them.

Decide when your NPC was deafened. If it was over a year the past, they probably learnt to read lips, but they may have trouble with characters with an unfamiliar non-human facial structure, or just big wiskers. Even with readable faces, it is impossible to tell 'B's from 'P's, 'Z's from 'S's, and so on. Would they be upfront and ask the PCs whether that name is with a 'keh' as in 'card' or 'guh' as in 'guard...ian?' Or would they just appear rude talking through people they don't see, and mispronouncing the unfamiliar names. If they are not telling, is it because of shame, or because it is too much trouble for some temp help that haven't maimed themselves for master the way NPC has? Will they be in the campaign long enough for the PCs to figure it out?

(I myself rarely share when my tinnitus acts up, because that is boring; if I'm bothering to read your face it is because I want to learn something new.)

Also consider deaf people are able to notice some forms of sound. If something heavy falls, that shakes the floor. Music with drums can likewise be felt. Many people who are legally deaf can hear some tones, just not enough to make out speech. What is the exact nature of the curse? How does it interact with magic and illusory sounds, if your setting has such?

Basically, like TookyG said, do some research. But this may help you start the mental research on deafness on your own.