I don't believe there is any way to see the calculation of the tile yields, but its generally not that hard to figure it out yourself.
There is a handy page here that describes all the details on tile yields, but the general rule of thumb is:
- If it's green it gives more food
- If it's a hill it gives more production
- If it's got some other feature on it then it gets an additional gold/food/production bonus depending on the resource
- If it gives something that is not gold/food/production then its getting a bonus applied from either a natural wonder (always within one tile), a wonder (always in the city), or a religion/pantheon (you can check for this yourself.
That's pretty much all the possible inputs for tile yield calculations.
EDIT: As of the Winter 2016 update, it seems it no longer works the same way.
From the patchnotes:
Cities can no longer receive yields from more than one regional building per type; they take the highest (ex. production from multiple Factories)
Cities can no longer receive amenities from more than one regional building per type; they take the highest (ex. amenities from multiple Stadiums)
Answer BEFORE Winter 2016 update:
First off, you can actually directly see the various bonuses by hovering over your city's production. (same for food, faith, science, etc.)
I found out that
A) The bonus does stack, a factory gives +3 production, a city with a factory of its own within range of another factory has +6 instead of +3, thus receiving the bonus.
EDIT : This bonus CAN stack multiple times:
As you can see here, my Capital is within range of 3 different fully upgraded Industrial districts, so it receives +9 from factory (+3 from each) and +12 from power plants (+4 from each).
B) Only the factory bonus was added to cities within 6 tiles, NOT the whole zone bonus. So say a city with no industrial district is in range of an industrial zone with a factory and a workshop, the other city will only receive the +3 bonus from the factory. Again, as you can see in the screenshot, my capital does not have an industrial district of its own, so it only receives bonuses from Factories and Power plants, not from the workshops.
This makes sense as the entertainment complex, for example, has multiple buildings that extend their bonuses. So each building is worth building, as each will only give off its own bonus.
Best Answer
tl;dr: you get the base resource, but the resource doesn't count as being "improved" in any way.
As a Stack Overflow user, my first thought is to check the documentation. (Yes, there is a manual.) According to page 48:
(emphasis mine)
It's not clear whether the city gets the additional improvement bonuses, such as counting for adjacency purposes.
That didn't satisfy me, so I ran some tests.
I found a spot with a mine-able resource (niter, base 3 food/1 production) next to empty regular grassland (just 2 food). After I built the city on the niter, I saw niter appear in my nation's list of available resources, but the tile continued to produce the same 3F/1P. When I reloaded and built the city on the grassland, then built a mine on the niter, it started to produce 3F/4P instead. Conclusion: cities do not count as resource improvements (i.e. mines, pastures, &c.)
To test adjacency, I placed a farm immediately to the right of the grassland city, which was a rice grassland hex. Its base value was 3F, and the farm boosted its production to 4F. Then I started another playthrough where the city was not adjacent to either hex, and placed farms on both hexes. The production went from base 2F/3F to 4F/5F after the farms were built. Conclusion: cities do not grant resource adjacency bonuses (which really isn't a surprise since we already know they don't count as resource improvements in the first place).
I did this with a game starting in the Information Age (just so I would have the farm adjacency bonus available for testing) and the leader Catherine de Medici of France (because she doesn't have any special abilities that would interfere with these tests).
Side note: when I put the city on the regular grassland hex, the hex gained an extra unit of production. Based on the available evidence, I don't think this has anything to do with resources; I speculate that it's the game's way of making sure that no city starts with 0 production (and ends up in a sad, perpetual state of never being able to build anything at all).
EDIT:
Hey, I have points now, so I can include the screenshots I took. You can see the city doesn't improve the niter yield at all, nor does it provide/receive an adjacency bonus to/from the farm.