Is anything required of someone who intended to perform 'Umrah at the beginning of Ramadan, then changed his mind and traveled to Jeddah, then intended to perform 'Umrah again from Jeddah, entered into a state of Ihram from his home there, and proceeded to Makkah?

If you pass the Miqat without the intention of performing 'Umrah, you are not required to enter into a state of ihram from it. This is based on the statement of Ibn 'Abbas (may Allah be pleased with him): "They [the Mawaqit] are for them [the people of those places] and for those who come upon them from other than their people, among those who intend Hajj or 'Umrah." Therefore, your entering into ihram from Jeddah is valid, because you formed the intention for 'Umrah from there.