Philosophy is fundamentally the search of deeper meaning in the universe, in ourselves, and the general study of problems concerning a vast amount of issues. But I think you are correct. You can only verify scientific philosophy with math and physics, not really explain it. Then again, each lay in the same realm of existence and each have to do with each other. I, myself, prefer more applied philosophy as you seem to as well. :3
As for your second one, I partially agree with you. Anger gives you great drive, correct. It allows man to push forward immensely beyond our limits. Then again, other feelings and states can do the same, such as grief or excitement or Love. When it comes down to anger, however, how far is one willing to take such? Harvesting the energy and using it productively is one thing, but using it to hurt another is something completely different. And pure hate can have tremendous effects on the human body and mind. But pure hatred, I believe, one cannot control. It is a blazing forest fire, merely engulfing all in it's path.