And as such, any Federal law enforcement activity in his county had to have his approval.
No one answer can fit all here. In some counties, the Sheriff is busy enough and doesn't need the distraction of worrying about Federal Agencies. Federal Agencies carry out law enforcement activities all the time without notifying a given County Sheriff. BUT, as chief law enforcement officer in the County, a Sheriff is within the law to demand that other law enforcement agencies have a search warrant if something about what they're doing is suspicious.
My belief also, is that if a Governor of a State has evidence of Federal malfeasance, he can withdraw the peace officer status of Federal officers in his State. You can see the problems with this though. If a search warrant is to be served, Deputy Sheriff's will have to serve it, thus dragging the local Sheriff's Department into cases in which they have no real interest.
Democrat Governors might revoke the peace officer status of Federal officers during a Republican administration, and Republican Governors might revoke the peace officer status of Federal officers of a Democrat Administration. Presently both sides generally leave well enough alone.
Incorrect. The sheriff is the highest elected official, chief law enforcement officer in the county in which he resides etc, etc, in those states where the state constitution declares it so. Some do, some don't. It is not uniform from state to state.