Does he who says, "For God's sake, don't come" or "For God's sake, don't go with me," become obligated not to come or not to go?

There is no obligation for someone to whom it is said, "By the face of Allah, you will not come," or "By the face of Allah, you will not go with me," to comply with this statement, whether it is an oath taken upon him or a request made to him by Allah. Fulfilling the oath of one who has sworn and answering one who has asked by Allah are commendable acts, but not obligatory. It is sunnah to fulfill an oath and to answer a request made by Allah, by analogy with swearing by Him, but this is not obligatory.