How is it that Redridge didn't hit Eli when shooting at him in the town shoot out?
Redridge fired one shot at Eli with his pistol and by the sounds of it, completely missed. The second shot, he took his time, gripped his pistol properly, aimed, fired and if you notice he hit Eli in his backpack. At this point Eli turned around and a shoot-out with Carnegie's men ensued. If we are going with realism here, it could be said that improper maintenance caused the pistol to be significantly less accurate, so even if Redridge was aiming directly at Eli, if there was a significant amount of dirt or build-up in the barrel, it could cause the bullet to stray far off course. This would explain why Redridge looked at the gun after he fired his first shot. As for the shot hitting Eli's backpack, it's possible it hit something inside his pack which stopped the bullet. Possibly one of his machetes, the bible, or something else. If you want to go with certain mystical qualities the film presents, it could be said that divine intervention stopped the bullets.
Alternatively, several scenes hint that Redridge may be a reluctant killer in a brutal world, hiding a good heart beneath a normally uncompromising exterior and that he found himself unable to kill Eli without flinching at the last second and missing.
Why did Eli have to show everyone the back of his hands? What was the significance of that?
The reason he had to show his hands was to prove that he was not a cannibal. If someone consumes human brain and nervous system tissue, such as the spinal cord, they risk developing "Kuru", a disease related to Creutzfeldt-Jakob (aka Mad Cow disease). It is caused by warped proteins called prions, and causes small holes to form in the brain of infected individuals. The disease causes trembling and shaking all over the body, which worsens over time.
It isn't stated but it's implied he died from his gunshot wound. He was shot in the gut and if he didn't receive proper medical care, he would have died slowly, but definitely would have died eventually.