My father has a bad temper too. But usually I was the cause of his angry. Many people said that I am quite naughty. I have never paid too much attention to the color of my father's eyes because I didn't have enough time to observe that. What I know was that he was going to beat me, so I had to run as quickly as possible. Mmm... never want to pay attention to that.
When we get angry, the pupils of our eyes will dilate. To our Asians, our eyes will become darker because of the dilated pupils. But if you mean the eye color will turn from blue to green or other kinds of colors, I think that's impossible. Sometimes, if our eye color changes dramatically and suddenly, it can be a sign of some kinds of diseases. We may need to see an eye doctor immediately. But the color of our eyes will change slowly as we age, and that's quite normal. Hope this helped!
We may get red eyes when we are very angry or sad because we may cry or the ups and downs of our emotions will increase the blood circulation in our body. And the blood vessels in the whites of our eyes may dilate so we may get red eyes. But that's quite normal and it will not do great damages to our eyes.
The eye color may changes in anime or in some kinds of movies. But that doesn't happen in our daily lives. The color of our eyes will change slowly as we age because the pigments in our eyes will increase or decrease bit by bit. But that often takes a long time to achieve that result. Usually it takes years or tens of years to change just a little.
No, emotions will not change the color of our eyes temporarily. So I suggest you to take your father to see an eye doctor immediately. I doubt that whether he has some kinds of liver problems because bad temper will lead to some liver problems. And the liver problems can result in yellow eyes (the whites of our eyes will become yellow). So I think he'd better see an eye doctor immediately.