6. is a non-elected official with no real power, however they usually choose and carry out a specific agenda while they hold their office.

I believe you could be referring to the spouse of the President, also called the First Lady of the United States. The spouse of the President is non-elected and not confirmed by the Senate. Although she does not have real power, she can be very influential and has a prominent presence in the live of the nation.  

a is correct

hope this let me know if it is right