Hi

I dont station family members in towns to maximize income. Particulary as Brutii with those great cash flows they develop as they take over the Aegeon.

I typically move them around so some spend time in the city with an Academy. Move them around to swap ancilleries. Move them towards the front so they can lead armies of conquest, or so they can beat up rebels.

As for the trade income part of the question:
"will trade revenue ever decrease or not be affected by a 0 maint governer? Or will trade/rev always increase when you have an actual governer in the city, regardless of how much or how little management he has"

Trade revenue fluctuates based on
1) the trade routes in operation
2) the population of the cities involved
3) appearance/disappearance of the slave resource
4) rebels (but not pirates)
5) gaining or losing trade rights with other cities
6) buildings
7) governor skills, traits and ancillaries

1) Routes fluctuate. You might blockade an enemy city and a trading partner may now choose to trade with you instead.
2) Population change due to growth or recruitment impacts income..in both cities.
3) Enslavement creates a slave resource for 20 turns. If one city has it and another doesnt this is a tradeable resource (population doesnt change)
4) Rebels on roads reduce road trade income
5) Roman civil war for instance cuts Roman income dramatically as you can no longer trade with other Roman factions.
6) Buildings like temples, roads, ports can improve trade income
7) Governor skills and ancilleries will affect trade income.