I'm sorry you're struggling with living with your dad at the moment, and I hope your situation improves. My mother also mocked and belittled me etc. all the time (but she wasn't mentally ill; she was just bitter). Have you spoken (or written) to him about how this makes you feel and about how you might like to improve things?
But I ought to point out that some of the symptoms associated with NPD - such as a sense of self-importance, a need to be admired & respected, and a lack of empathy - aren't only symptoms of NPD. They can also be a teenager or young adult's misinterpretation of their parent's perfectly normal (if annoying) parenting behaviour. This does not mean that parents are automatically narcissists, nor indeed that they have a personality disorder.
Your dad, who has been a parent for several decades, has grown accustomed to being an authority figure in his own house. He expects that his kids should love and respect him. As far as he's concerned, his word is law in his house. He knows for a fact that he has more life experience than you, and so he believes (probably correctly) that he knows more than you do, which is why he thinks he's right all the time (probably incorrectly).
These are all perfectly normal things for parents to do. But it sucks to be on the receiving end, especially when you're an adult.
But it seems to me that the way he's behaving towards you now has been pretty much unchanged for years; i.e he hasn't altered his parenting style to adjust for the fact that you are now a grown adult and thus he is still treating you like an unruly teenager. There's also another possible angle: some men engage in dominance behaviour when challenged by other men. Now that you've come out as a trans male, it's possible that he's being extra-aggressive so that he can maintain his place in the pecking order. So that, I think, is where you need to focus your efforts, rather than on trying to guess which mental health conditions he may or may not have.
You need to renegotiate your relationship with your father. It might be very difficult to do this whilst you're living at home because you're in a position of relative weakness, so you may need to move out if you can. He's not going to see you as the adult you are until you start asserting yourself as one... and gaining your own independence is the most convincing way of doing that. If you're currently not able to work, are there any charities or LGBT associations in your area that could help you with housing etc.? Could your social worker help, especially if you tell them that you are not able to continue living with your dad as it's adversely affecting your mental health?
If your dad does indeed have NPD, that can only be diagnosed & treated by a mental health professional. All you can do is to tell him you're worried about him, and encourage him to see his doctor. But as for you: you would probably benefit from seeking help to deal with your anxiety & feelings of paranoia. These can improve on their own, particularly as we proceed through transition, but it probably wouldn't hurt to ask your doctor for a little help to get you through this difficult stage.
