Question

The authority of the supreme court hears cases decided by lower courts? true or false ​

Answer 1

Yes they do so the answer is true

Answer 2

This question is worded poorly, so it's hard to tell what info you need, so I'll go with this:

The mandate of the Supreme Court is not to make law, but to interpret law, and to conclude whether or not a judicial issue is reflective of the spirit and word of our laws as defined and laid out by the U.S. Constitution.  They will only hear cases that in some way hinge on an issue of Constitutional law which is unclear in some degree, or may need to be clearly defined as a means of clarifying how the law should be/is intended to be applied and practiced in our country.