I'm interested in creating some construct of a society in the Twilight and Midnight zones of the ocean. By what means could they mine, farm, and trade in what is suppose to be a more futuristic society?
Buildings: Large steel domes filled with air would be the most durable building on the bottom of the ocean. Glass would be risky since a small crack would create a huge problem.
Mining: Drilling for oil in underwater deposits would be way easier if the oil drill were sitting on the ocean floor.
Kelp has a high rate of growth and its decay is quite efficient in yielding methane, as well as sugars that can be converted to ethanol. It has been proposed that large open-ocean kelp farms could serve as a source of renewable energy. Unlike some biofuels such as corn ethanol, kelp energy avoids "food vs fuel" issues and does not require freshwater irrigation.
O2 production: It would be hard to obtain oxygen from the ocean's surface, so lakes full of phytoplankton would be the easiest way to produce oxygen for the people to breathe.
Transportation: To get in and out of these colonies, you could use an airlock into a pressurized room with a hole in the floor through which submarines could be accessed. The layout would be similar to a beaver dam's entrance, enabling open access to the ocean without flooding the colony. A water-lock would also work well. (like an airlock for water)
this theoretical society could farm bacteria from artificially created vents. These bacteria cultures could be developed to feed many people. These would be the only food that could be developed in bulk to feed the deep sea masses.
This is essentially the same as planning to build a habitat on another planet. The most reasonable means of farming and food production are exactly the things we are planning to do in space.
Hydroponics and vertical farming allow for efficient food production. With that you could grow just about any fruits and veggies outside of large crops like grain and fruit trees.
Many projects have taken to developing food from hyper-nutritious algae, if you wanted to lean more towards the ocean farming idea, but that would still be enclosed as the right kinds of plant life likely wouldn't survive at that depth.
If you were hoping for something along the lines of farming on the sea floor, then I really don't know of anything that could be grown in that sort of environment, except for maybe hunting for bottom feeders. In that case the shellfish business could be good.
I like the idea of an artificial sun inside a dome to provide energy, heat, and light. Of course, there may be some practical difficulties. Perhaps a more regular fission plant with sun lamps would be more feasible.
To make the domes work, consider increasing the pressure inside the dome to match the ocean pressure at that depth (saturation diving). Note that this requires a lower oxygen percentage and uses helium instead of nitrogen and most other gases typical in air.
A nifty side effect of the higher pressure is that you can use moon pools instead of air locks to get into the sea.