Why can some people move their ears while others can't? Why can some people roll their tounge or contort it certain ways?

 

Also, why can I lift up the left corner of my mouth (while keeping the right side down) but not the other way around?

 

Why why why!

It's probably either genetic or practice, depending on the ability. For example, the longitudinal folding of the tongue is definitely genetic (i.e. no amount of practice will allow somebody to do it, who cannot do it to begin with). The moving the ears thing is probably down to practice. Most people make that movement when they laugh (thus most people can do it), and being able to do it deliberately is simply a matter of practice.