May the President pardon himself?

Article II §2 of the Constitution states that the President  "shall have power to grant reprieves and pardons for offenses against the United States, except in cases of impeachment." It also states in §3 "he shall take Care that the Laws be faithfully executed." This defines his power with respect to law. He may not make, suspend, or repeal laws, but only execute them. He is not a monarch, and it is a source of confusion to take a term out of British monarchical practice and carry it over to American constitutional practice. That change in context changes the meaning. 

The Constitution also states in Article II §2, "The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States." That is essentially synonymous to a right to "equal protection" of the law, which was included in the 14th Amendment.

What is a pardon, for a president? Not for a monarch, but for a president. It is simply his determination not to enforce a criminal conviction and sentencing order of a federal court. It has no meaning until after there is a conviction, because the crime is  not defined until then. Nor may he issue a pardon before conviction as a way to prevent a trial. He has no power to prevent a trial, including a trial of himself, although the court may not have personal jurisdiction over him. Nor may he use it to remove personal jurisdiction from any other individual. A court has personal jurisdiction if the defendant appears in it, unless it is a special appearance. 

A pardon is not a reversal of a conviction. Even after a pardon the conviction stands, and may be enforced at any time, until it is reversed. A president cannot bind his successors, any more than a monarch may. His decisions and determinations expire when he leaves office. (That includes executive orders.) So, yes, he may pardon himself.

But the pardon doesn't last forever. The conviction may be enforced when he leaves office.