No they don't. They may get general outlines, like fight the war on drugs, but then they are pretty much free to meet that outline in the manner they feel is most effective. Government has never been in the habit of micromanaging every department, otherwise nothing would ever get done.As far as I can see, they run their own programs.
No they don't run their own program
They run the program they are told to run the way they want to run it. But they get basics and authorization from higher up.
Wrong they had to get the authorization to allow guns to leave the United Sates into another country. no department has that authority to do it on it's own.