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.