What are the materials and their percentages? Is there cotton?

There's a saying when you're hiking "cotton kills"... this is a lightweight fabric that is designed to resist water but still be breathable, they resist stickers and thorns. The fabric dries fast and the pockets have a mesh interior so if water gets in them it drains. It's too bad the other person answering threw them away - they could have given them to someone who would treasure them for their intended purpose. I'm not certain of the exact makeup but I would assume some type of poly/nylon with a bit of spandex for stretchability. When I go to places like Puerto Rico all I bring are these pants, I just get in the water to clean them up and am dry in a short while. Daytime the legs come off to stay cool, when the sun sets I zip them back on for bug control and to stay warmer. Super easy to wash, I run them through the washer with my other clothes. They are very durable but if you're allergic to synthetics, these could be terrible...

Do they unzip at the bottom of the leg for easy pull off?

No, they only zip off at the middle of the leg.

Do these pants shrink when washed and dried?

They did not shrink for me after washing and they are almost dry when they come out of the washer I just put them in the dryer on air only so they don't drinker much.

i need 34x36 what size should i order?

These fit really true to size for me. I'm a slim 30" waist (or even a 29") and ordered 30's. They fit great and if I'd have ordered smaller, I think the elastic waistband would be annoying. For lenght, defer to a bit longer as they can cinch up around the ankles. Perfect over hiking boots.