Cedre
Selfless acts can easily be explained by evolution. For most of our human history we lived in small groups where we would have known and been closely related to everyone we saw. Therefore it helped to pass on our own genes if we had empathy with those around us and looked after their welfare. Many other species also demonstrate strong evidence of such empathy.
Empathy is inherant in us as a consequence of our evolution and so we continue to apply it instinctively even in the modern world where we see and meet people on a daily basis who we don't know and will never see again. However, I like to think it will stay with us and remain important as a kind of goodwill currency. Even though we will never know most of the people in our large modern communities, if we all treat each other well we will all benefit.
As the saying goes: What goes around, comes around.
As for your question about forgiveness, I would say that holding on to an emotion like hate produces a lot of stress, and letting go of that can produce the feel-good emotion you talk about.