Re: Roads and Railroads
A road passing over a Village that is also connected to at least two cities gives the Village hex +1

/

. A railroad in the same situation gives +2

/

. However, roads cost

to maintain and railroads cost 2x

to maintain as roads, so really what you are getting for building roads through Villages is negating the maintenance costs and getting a little net production.
If a city is connected to your Capital (via a road, railroad, or Lighthouse) then that city produces a little bit extra

per population living in the city. There are buildings and wonders that can increase this gold-per-citizen ratio, but by default it is a pretty small amount of gold. This city connection

DOES count towards the

output of the city, however, so it does help with poverty which is why cities not connected to the Capital will in general suffer from more poverty.
Upgrading roads to railroads should have no direct impact on city unhappiness from poverty (save for the small boost to gold output from Villages), but it will decrease your empire-wide gold per turn due to the doubled maintenance costs.