Does every state in the USA have a State Attorney General of their own? What exactly do they do? ?

Each state has its own.  The current V.P. was the first female attorney general of the state of California. They are the head of the Justice Department of the State. They represent state interests and when there is a conflict with the federal government they may sue the federal government on behalf of the state. 

The federal government also has its own top law enforcement officer called the U.S. Attorney General. They head the federal Department of Justice. They are suppose to represent the interests of the citizens at large and not suppose to act as the personal lawyer of the president. When Barr was the A.G. he crossed that line and gave the Department of Justice that he ran a bad name. 

William Barr was the US Attorney General, not a State Attorney General.  Yes, each State has an Attorney General.  That person decides what is and what is not in accordance with STATE law.  This has GOT to be homework if you can't look it up yourself.

 Each state has an attorney general who is the main legal advisor to the government of that state.  In some jurisdictions, attorneys general also have executive responsibility for law enforcement, prosecutions or even responsibility for legal affairs generally. In practice, these things vary between states and countries that have attorneys general.

In some cases the Attorney General is  largely equivalent to that of a Minister of Justice in other countries. Bill Barr was the United States Attorney General and held  ministerial responsibility for legal affairs in general for the US government meaning that not only did he advise the government on legal matters he was a member of the Cabinet,  head of the Department of Justice, plus the top law enforcement officer and lawyer for the government.

William Barr was the "United States Attorney General".  He was not a "State Attorney General".  A "State Attorney General" runs the justice or law department of one of the states.  The "United States Attorney General" runs the Justice Department of the federal government.