Should "air roots" be put into the planting soil when being transplanted, or trimmed off?

No, don't cut them off. When you transplant your orchid, try to replicate how the plant looked in the old container. Make sure all the air roots are out of the soil. Apparently the plant takes in some nutrients from the air as well as the soil. I use an orchid liquid fertilizer once a month (diluted in water, instructions are on the bottle). They also don't need that much soil/orchid compost. The main thing to do, though, is not over water them. Mine are happy when I have plunged them into sink full of water, flower pot and all, when they get dry.