Most definitely yes. That person would feel the air being cut off, and the intense pressure the rope would put on the neck. It wouldn't act as a magical cushion.
Absolutely! It probably feels like you are drowning as you are unable to draw a breath. Don't try it! And it's an awful way for your family to find you as your entire body relaxes and releases all of your fluids! If by some chance you don't die, you'll end up paralyzed or worse!
It depends. If the drop is "just right", the neck is broken and causes near-immediate unconsciousness. If too short, death by strangulation occurs, which is relatively long and painful. If too long, death by decapitation occurs, which is relatively painless but leaves rather a mess for your next of kin.
Please don't hang yourself. Chances are you could have a long, full, rich, interesting life, regardless of how dark it may seem today. If you are considering this, please, PLEASE talk to an adult (parent, pastor, counselor, or whoever) that you trust first.