I'm having trouble determining what generates/produces more production points and where.

The planetary factories seem to quicken the production points on buildings but not so much on ship production

I JUST discovered that the stations, with those building modules, increases ship construction (points?) and reduces build time and cost. It was taking forever to build things with just battle stations.

How much, if any, do planetary factories affect ship production?

Does the Planetary Mineral rating affect Building/Ship construction time? (aside from the general minerals produced)

On the subject of buildings. I’ve noticed the build time, for say a Mine, costs 120 (or so) and I can build it (buy it off) right away, but the next one cost exponentially more Is this how it is supposed to be? Is there a scale I can understand that may be on the forums already?

Production is generated by population and factories. In the planet screen, you can click on a population icon to see what that race's yield is (it's usually 2 per pop), and you can click on a factory to see a detailed breakdown of the planet's production and how much each factory yields. (You can also do this for any building type or any of the yield icons.) The output of each factory depends on its technology level and whether it is fully staffed.

Factory production applies to all projects, including ships.

Construction modules for orbital stations are required to build certain size classes of ships (you need one to build cruisers, and two to build capital ships), but (unless I'm mistaken) they don't directly affect production yield. Shipyards reduce the construction cost of ships to 70% of their base cost. You can think of ship construction as parts being produced on the ground, and then assembled in orbit.

Planet mineral rating affects metal yield, but not production. We've just added Mineral Rich and Mineral Poor icons to the solar system display to help you tell which planets have abnormal mineral yields.

Successive copies of each building type cost proportionally more than the previous one. So, your first Lab will be cheaper than your second Factory.