Presidential Line of Succession:
The Presidential Succession Act of 1947 sets the order of Presidential Succession. This order is followed if the President dies or is incapacitated. The order of cabinet officers included in the list is determined by the dates on which each of their positions was created:
Vice President
Speaker of the House - Paul Ryan
President pro tempore of the Senate - Orin Hatch
Secretary of State - John Kerry
Secretary of Treasury - Jack Lew
Secretary of Defense - Ash Carter
Attorney General - Loretta Lynch
Secretary of the Interior
Secretary of Agriculture
Secretary of Commerce
Secretary of Labor
Secretary of Health and Human Services
Secretary of Housing and Urban Development
Secretary of Transportation
Secretary of Energy
Secretary of Education
Secretary of Veterans Affairs
Secretary of Homeland Security
Orders of succession are also established for each of above Cabinet officials within their own departments. Ten successors residing within the National Capital Region (NCR) and three successors outside the NCR are identified for all executive departments and agencies. Here is an example of a 2013 Secretarial Order of Succession.
The Whitehouse has released this information dated 1/18/2017
https://whitehouse.gov1.info/continuity-plan/
Question- Has any of the new cabinet been approved by the Senate?
The 25th Amendment, not the Presidential Succession Act of 1947, covers when the VP becomes President or Acting President. The PSA covers the rest, but there are questions regarding its Constitutionality (search “Presidential Succession Act” and “unconstitutional”).