First American pope elected and will be known as Pope Leo XIV

Is Pope Leo eligible to be voted President of the United States?

Is he the first US Citizen to be head of a foreign state or have their been others?

Edit: Did some googling and found Toomas Hendrik Ilves was a naturalized US citizen who renounced his citizenship before becoming an Estonian ambassador and later President of Estonia. Not seeing any who actively held US citizenship while being head of state.