Some people have a phobia about snakes. It is usually induced by some subconscious fear they picked up before they could really understand things.
Snakes generally avoid humans. They really are more afraid of you than you of them. There is also a myth about how quickly they can strike. Actually a human's reactions as quicker than a snake's - but don't make a habit of testing this out.
If a person is bitten by a snake it is usually because that person has accidently put their hand into or under something where the snake might be resting up.
Years ago, I was stationed at a place that had so many poisonous snakes that we had a door at the front of the outside John and a hole in the back wall. The snakes would come inside to lie in on the cool concrete floor. As they heard you coming along the path, they'd wake up. And as you opened the door at the front you'd sometimes see a tail disappearing through the hole in the back - the serpent's tail.
No, snakes generally avoid people. And of course they have eyes. Can they climb walls? That would depend on the wall: how high, how smooth. Would they want to? Depends whether they expect they'd find something to eat on the other side. They can figure this out by both smell, and by feeling the vibrations given off by little rodents such a field mice.
Generally, snakes like warm weather. They like to warm their bodies on heated rocks, warm patches of earth and the like. They are reptiles, after all; cold-blooded, needing warmth before they can become reasonably active. Thats why you find most of them in warm climates.