If you only have one of the class prefixes (.col-xs-9), does it only apply at that screen width?

Are items full width unless specified?

Do class prefixes apply at the smallest size and above?
yes.

My columns are getting the right size, but not all the bootstrap styles.

What is a clearfix?

Developing with bootstrap is semantic - classes you apply have a readable meaning.

If you want to try a Bootstrap sandbox, create a new codepen and add the Bootstrap css.