I think during Watergate the question arose as to whether a sitting President could even be indicted. Nixon became an unindicted co-conspirator so as to avoid having to answer this question.
The Secret Service is under the Department of Homeland Security, which is controlled by the Secretary of the Department who is appointed by the President.
The President starts the interaction by stating, "I pardon myself of any crime for which you received a warrant, thus invalidating the warrant, and you, your boss, his boss, and the Secretary of the Department of Homeland Security are all FIRED! Please leave before I have the rest of my protective detail shoot you."
:-)
The President cannot use the executive pardon power to prevent his own impeachment or removal - the Constitution prohibits the President from acting as his own judge.