I think the most common hair color is brown, what do you think?
You're close! Technically, black is the most common hair color. Brown comes after that.
I would think there are many different shades of brown hair between light brown and dark brown
There's a lot of variation, especially between different hair colors. Brown hair has high levels of a dark pigment and low levels of a pale pigment.
I wonder if two people with brown hair can have a child with different color hair than its parents
That's true. If they both have a recessive gene for blonde hair, their child can be blonde!
I wonder in which parts of the world brown hair is most common
Well, it's pretty common in Europe and the U.S., as well as a few other places. I live in Canada and see brown-haired people all the time!