Resources are empire-wide, provided there is a connection by road or territory between the available resources and the area where the units are being raised/resources being used. We may run into some issues when empires start spanning oceans, but I will rule on that then. (However, I expect that unless all sea routes between two owned territories are blockaded, they will count as connected for any such purposes).
For example: if your empire consists of Lester North, Lester Central and Lester South, you can have an iron mine in Lester North and still build swordsmen in Lester South. If Lester Central rebels and becomes neutral, you can only build iron-dependent units in Lester South if there is a road between the two territories. If Lester Central is taken by an enemy empire, you cannot build iron-dependent units in Lester South because it does not have access to iron (unless it acquires it from another source).
Roads count for connecting resources, if they are through neutral territories.
I am considering industry limitation per territory at the moment. I think we will go with one industry/territory (the limit can be increased with infrastructure research), but I will rule on this for certain next turn.
I will rule for certain on underground farms when research on them is completed, but my gut is suggesting (read: not my final ruling) that they will allow you to build farms in areas that do not contain grain or other farmable resources. However, this will count against the probably industry limit in a territory. Obviously, barren territories you build underground farms in will not get the revenue bonuses from the grain resource or similar. Underground farms might also not get the benefits of ordinary farm improvements (from researching the higher tiers of the Agriculture tech) without more underground farm research.
The base cap for research is secret. Each turn anyone invests £500 or more into a tech, the base cap will increase by 1. Each side that successfully researches a tech causes the base cap to increase by 10, until five sides have researched it (whereupon it becomes Public Domain and everyone else gets it for free).