1) For the bullet to penetrate anything, it must have the majority of the energy in the universe. Likewise for the armour that nothing can get through; it must have the majority of the energy. There can't be two majorities.
2) Either it is the fountain of youth which stops ageing but does not prevent death by accidents such as drowning, so yes, or it is prevents all death, so no.
3) I don't accept it. Oh, look, I completed it. Do I get credit anyway?
4) My resolutions to this temporal paradox:
a) The universe implodes
b) It is in a separate timeline distinct from the original but identical in every way up to the time travel but diverges them, any action there would not affect her as she came from this universe, they would only affect the girl in the other universe.
c) The laws of probability will warp as she gets close to killing her grandmother so that normally improbable events will occur more to ultimately prevent her from killing her
d) She ends up not being born but then is spontaneously called into existence with all the memories she would have had had she been born, specifically to use the time machine and kill her grandmother, then ceases to exist moments after.
5) Which is why weather people who say it will be twice as cold or twice as hot are stupid
6) It won't be.
7) Your car will cease to exist before reaching the speed of light as all it's matter will be converted to energy
8) Proof of the nonexistance of god. QED.