Your plant is a kind of century plant, Yucca filamentosa. This Q&A has some tips about pruning it, although note that the advice is in response to a question about how to get rid of this plant, so it's not all directly applicable to you. Here's another Q&A with some info about pruning. Basically, you should trim off the flowering stalks after they're done flowering, and remove any dead leaves. But other than that you can pretty much leave this plant alone and it will take care of itself. The spotty leaves on your plant look normal to me, and not diseased or harmful to the plant, so I would leave those.
Yucca filamentosa reproduces by growing young plants (or "pups") from the roots, so the small one off to the side is probably a baby plant. I would leave it alone. It should eventually grow large enough to share space with the parent plants, and since they're joined at the roots it won't starve due to lack of sunlight.
If you want to relocate the small one, you can probably do so successfully. The roots are quite tough, so you might need a saw to cut the rhizome that joins the baby to the parent plant. Here's a guide to dividing yuccas.
