It’s live per the description. Nice sourcing, they saved you months of phosphate curing wait. The growths on the rock means it’s alive, plus thats 3x as long underwater as a cycle chart shows for completion. Adding ammonia won’t hurt, theres not heavy worm and hitchhiker loading in that type of rock. It will be a neutral impact to add ammonia, same outcome if you do or don’t add some, the rock is already covered in bacteria for the benefit of being already cycled when you buy it
taking it home doesn’t kill the bacteria, it transfers well
Adding bottle bac would not be indicated at all, already paid for live rock. The media is also neutral. To run lots or to run none has no effect on your tanks ability to carry fish, the sand and rocks have it all covered. Using media will not hurt, nor will not using any. If you added it now vs later will not matter at all, it’s neutral impact to run meaning there’s no parameter that will be out of line and then fixed by adding media, the params will be the same with or without the extra surface area.
the habit to pack extra media comes from freshwater, where internal surfaces are slicks vs high surface area like reefs. One benefit of running none is you can clean out settled waste easier to remove it from the system. Another benefit to not running media is you can make the area a zone for other inclusions like an algae scrubber or pod refugium etc
running the sump with floss frequently changed out as an export approach is common, that has measurable benefit vs typical media that sits there daily uncleaned
