1. Don't headshots travel downwards? So it might have entered his head higher than the spot, but it could have reached it. 2. Same thing happened with future Peter in IABD - the Haitian left, he remained dead.
1. Isn't the spot in the brainstem, lower back of the head? Anyway, the bullet could still have moved there. 2. Wouldn't they show that? And the same could have been done with Arthur 3. Doubt they'd repeat the "he's dead, no he isn't" SL
2. No one knew he had regen? Yeah they did. Everyone who'd known Peter would have known he'd had regen and so Arthur must have regen after stealing it from him
A bullet between the eyes would rip out a lot of Arthur's brain as it would most people so even if he somehow did survive he would think himself a grapefruit for the rest of his life and spend the rest of his life in a mental home. Plus Rene being present didn't actually do much when Sy walked in as he could not hold back the abilities and then Sy killed Arthur but even so Arthur would have been cramated by the fire.