Hi and welcome to RG.

PVD and DLC coatings are coatings applied to the steel cases that give them that dark (black) appearance. Although the results of PVD and DLC are similar they are completely different processes and DLC is far more durable than PVD.
AR coatings are anti reflex coatings applied to the crystals in very much the same way as eye glasses have lenses have anti reflex treatments. This reduces the reflectivity of the crystal making the dials more readable in some lighting conditions.
As to waterproofing of your watch, sometimes a little silicon grease and tighten up the case back and crown is all it takes, others it takes a little more, it varies from model to model. I would recommend that you have your watch pressure tested at a local watch smith before taking it for a swim.