Berghia Nudis are Obligate feeders, meaning they have 1 food source and will die without it. Their food source is Aiptasia. They also hunt in "packs," so several are needed. They will split up, searching for food. When they find it, they send out a signal and several of them will converge on a single Aiptasia. If you don't put enough in a tank, they won't find the Aiptasia, as effectively and will die before finding and eating them all.
Peppermint shrimp are a possible predator. I highly doubt Mandarins will touch them. Some Wrasses may eat them though. Bristle worms are also a possible predator of Berghia. However, Berghia hunt at night, when fish are sleeping. During the day, they hide in cracks, holes and crevices, in your live rock.
A very effective way to utilize Berghia, AND build up their population, is to keep them in a small container and supply them with Aiptasia. They'll quickly start laying eggs. They reproduce quickly. Once you have a decent population of them, place a group of them in your display tank, in the evening, high in the rocks. One thing to be careful of is to make sure that they get a good grip on the rocks, before releasing them. Usually, you'll be supplied with a small pipette, for this purpose.