When Harry was being saved by his future self, he was actually very lucky. Either of two things could have happened when Harry was being attacked: 1) He dies (loses his soul), and there is no future self to save him, or 2) He is saved, and then time travels back to save himself. Harry is actually very lucky that the second option happened.
Also, there is another way to think about this same “saving your past self” thing. If you find yourself being saved by your future self, you don’t need to go back in time to save yourself. Since you have survived, your own survival has been guaranteed, no matter what you decide to do. However, this means that what you were saved by wasn’t actually your own future self, it was instead your future self from a parallel universe, or not a future self at all. But since, you have survived, this fact really doesn’t matter. This is the point of view used in Orson Scott Card’s Pathfinder, which deals heavily with time travel.
The neat part is that when a man decides to save himself when any preventable, non-fatal bad thing happens in his life, he will prevent all preventable, non-fatal bad things from happening in his life, without needing to travel back in time at all. If it is unpreventable, it will happen anyway. If it is fatal, then the same idea in my first paragraph applies, with him relying on his survival in order to survive. Besides this, any man who has a time machine will automatically become the luckiest man in the entire world.
About your second question, it is helpful to think about time from your body’s point of view. No matter what the “world’s time” is doing relative to you, your own timeline moves foward constantly as you expirience it. As a real-world example, some muons and other subatomic particles seem to live longer than expected when moving at extreme speeds. Due to time dialation, the muon’s time gets slowed down. From the muon’s piont of view, the muon is living to the same age, but to the muon, the rest of the universe seems to speed up. From our point of view, it is the muon that slows down. From my piont of view when I travel back in time, I still expiriance time as normal. The “real world’s time” is just different from my time. If I die in the past, my past self still continues along my path, to die in the my past self’s future. It is only the “real world” time of my death that changes, not my time of death from my point of view. I put “real world” in quotation marks because time is relative to every object, and completely, perfectly empty space (as far as is known) doesn’t have a time flow.