1) Power generation
Plants will generate as much power as they need to to supply whatever demand exists for any
City Center in their radius. This radius starts at 6 tiles and is affected by Mexico City's suzerain bonus as well as Nikola Tesla, the great engineer.
It only matters that the plant aura can reach the city center; the individual districts themselves can be anywhere.
Plants
do not consume fuel just for existing. They have to be supplying power.
2) Fuel consumption
Fuel is used based on whole units. If you build a nuclear plant and it only powers one factory, it will still burn a unit of uranium. The extra 14 power just goes to waste from a fuel perspective (but not an emissions perspective, see below.)
Fuel use is based on each plant supplying power. (Some plants may not be supplying any and use no fuel.)
If you have two far apart cities each with a nuke plant, and they only each supply their factory for 2 power a piece, each nuke plant has to burn fuel to supply that power. Because a plant can use a minimum of 1 fuel, this means you end up using 2 fuel. If one plant covered both city centers, then you'd only need 1 fuel.
If you have multiple types of plants, which plant gets used is based on an order of priority:
Largest Stockpile of Resource
if a tie then
Largest resource income after unit usage
if a tie then
Most advanced power source (Nuke>oil>coal)
This can mean that if you have a full stockpile of everything, it will pick your biggest income - likely coal or oil- and use that. If you want to force the game to use nuclear power, you have to reduce your stockpile and reduce your income. The only ways to do this are to create coal burning units (counterproductive if you want to reduce emissions) or to rip up your coal mines. If you get lots of coal from city states then you are just SoL.
3) Emissions
CO2 is created based on how much
Power Load is satisfied by a resource, as well as what resource is burned to satisfy it. Coal is much dirtier than oil, which is much dirtier than uranium,
per unit burned. Because uranium produces 4x the power per fuel unit, it effectively produces a tiny amount of emissions compared to coal. Units that use fuel, by comparison, are always using the whole unit. Currently AFAIK there's no difference in emissions between using 1 coal to supply 4 power in a coal plant vs having a battleship consume 1 coal per turn.
@Victoria did anyone test units at all?
4) Plant production auras
All auras in the game currently allow 1 instance to apply, and it will pick the highest value for which aura to go with when multiple overlap. This is why you can have lots of factories at +5 aura, and use tesla somewhere, and suddenly see the cities near that IZ have +7 from factory.
There is no double counting of local and external auras. The auras for coal, oil, and nuke
do not stack.** They are all treated as the same class of power plant aura. The highest is used. For example, if City A has a coal plant that gives +2, and is in range of an oil plant in city B, it will actually get the +3 from the oil plant. If both cities and in range of a nuke plant, then they will get +4 prod instead from the Nuke Aura.
**The nuclear plant has a +3 science aura. This is treated as a separate thing from the production auras and so it
always applies to any city in range of a nuke plant. You don't need to make a weird matrix of oil and nuke and coal to maximize things. You can use nuke plants if you really want to min-max your science, but by that late in the game it's not as impactful so don't sweat it too much.
Which aura is used for production purposes has nothing to do with power generation. The production effects are provided if if you run out of the resource or aren't burning fuel.
Coal plants are local only; even with aura boosting effects like Tesla, they will never actually project their bonus.