Alright, so...
yes, you only add tokens to the city when a district is added or made more dense. This can happen during events, during the natural growth part of the event turn or in the topping out phase.
It is possible to have multiple factions and only one "citizen token" for power to go around. Then they do in fact squabble over what little power there is. This also is a yes on your question: Factions without power still exist. They just don't have a significant power structure or support to really affect too much.
You may also want to check out the devlog I posted the other day. I'm thinking about changing the power rules and the new set of experimental rules can be found there:
https://sharkbombs.itch.io/ex-novo/devlog/178994/overhauled-power-rules