Question

The President of the United States

has the power to lead the U.S. Postal Service under Article II of the Constitution

can appoint officials to the federal bureaucracy with the approval of the Senate

is required by law to follow a certain percentage of advisor recommendations

must assign the vice president as head of one of the Cabinet departments

Answer 1

Only the second. Aritlce II says nothing about the Post Office, which is a creation of Congress under its Article I powers. Congress has no power to constrain the decisions of the President by requiring him to follow this or that advice, because the President is co-equal to Congress. The Constitution says nothing about the constitution of the President's Cabinet. In principal the Senate could effectively compel the Veep to be appoitned one of the Cabinet secretaries by simply refusing to confirm any other choice. But they've never done that, and it doesn't seem likely they would, since there's no sense to it.