I think some input from Jan would be good, but my thoughts are as follows:
1. Yes, I prefer the latter as well, although I would like to differentiate Northern and Eastern from Southern, Central, and Western (all of which can share the same vanilla graphics) - at least until Gunpowder units come into play, at which point a general uniformity can exist across all european cultures. Colonial and Totalitarian, similarly, borrow Western graphics (individual civs can have culture graphics different to their culture type).
2. I think a reimagining is best, as shown
here. However, because these are culture based, I'd steer away from anything overtly identifiable (which is why I use the Greek Knight instead of the Roman Knight, as it seems more generic), so in many cases it might be best to use the Southern equivalent.
3. Presently, the Mesoamerican longswordsman exists
here, which uses the Macuahuitl (I assume). So, I'd say a similar stance should be taken where possible, using a culturally appropriate equivalent even where that doesn't necessarily reflect the craftmanship of the unit's weapons.
In most cases, Ancient-Medieval units are covered. What is sorely missing and would be a great help, however, are Warriors and Scouts, for which I have nothing unique but the Western/Central (vanilla), Northern, Mandala (IIRC, Sukritact made this especially), Andean, and Mesoamerican. I wouldn't need one for each culture, however, as for instance a generic Oriental Warrior/Scout could work for Steppe as well, and a West African one could work for Bantu, a Mesopotamic one for Islamic (maybe also Bharata), etc. Perhaps Workers and Missionaries, too, but I don't want to get ahead of myself