I'm not into psychology stuff but it is NOT normal.

My father is narcissistic but it's not one minute or the other. He acts nice in front of other people, and abusive when he is only with me. Like he would say I'm the greatest programmer ever when talking about me, but would tell me that I'm a failure and I don't know how to use a computer when I visit him and no one else is at home.

Suffice to say that if my mother dies first, I won't talk to him anymore and he'll be alone. But he will still complain that I abandoned him because I'm a bad guy.

Short answer: no, that's abuse.

It's entirely possible that he's a narcissist, from what you describe - especially if other people are saying that as well. Mind you, that's not the important part.

The important part is that this is obviously hurting you. And something tells me this isn't the only thing that he does that messes you up. Do whatever you can do get out of that household. It ain't gonna be easy, but it will be worth it. Trust me.

That sounds a bit like borderline.

I'm nothing like a psychologist though, just a possibility :)

My mom would cuddle with me and then yell at me

She is the person I'm most emotionally attached to, and simultaneously someone I'm terrified of...

He's still cut up over something that happened over a decade ago?

I knew someone who was like this; eventually they discovered lawyers, and all their relationships fell apart, including their marriage. They seemed to think that punishing someone by suing them (even if they lost — it was always their lawyers fault then) was a way of resolving their relational difficulties.