Was George Washington a major advocate of opposing factions in government via the Federalists and Republican parties?

No, in fact, he was against political parties. He felt that the political party would rule the elected official instead of the voter. That the party would become more important to the person than the people who elected him. For Washington a person was elected to office to help the "common good" and then to go home. If we look at our political system today I think time has proven Washington correct in his assessment of political parties.