So your phone gets warm to the touch when playing games? Yes that is normal. As far as the screen dimming, do you have the phone set for
Auto Brightness in the settings?? If so you can turn this off and place screen brightness all the way up if it's an issue for you.
If the phone is getting hot you may want to have it looked at. Also what GB is it? The larger GB phones will handle heavy use a little better then the smaller GB phones. More space. I find that after watching You Tube a lot on my 7 plus, that it gets a little warm. It's also in a case, and a heavy one at that. But it never has gotten hot. And yes it draws the battery down fast watching you tube for long periods of time.
As I said, battery drain quickly and a warm screen are normal. A hot screen and super fast battery drainage and you may have an issue with the phone. May want to take it to an Apple Store or call them at least and see what can be done. Depending when you bought it, it may still be under warranty. Hope you find a solution and Good Day.