I will respond in detail to the issue of fin nipping, after first agreeing with other members who have advise that larger groups of any shoaling fish is always going to be beneficial for the health and well-being of the fish...and can avoid any possible fin nipping. To that topic.
Shoaling fish need a group; they expect to be in a group of their own species, and this is programmed into their species' genetic blueprint. There are many species that we consider basically peaceful, and so long as they are provided with all of the environmental factors they "expect" (their genetic makeup), they tend to remain peaceful. This involves the size of the group, along with other factors such as the tank size (dimensions usually more significant that volume), water parameters, the aquascaping (involving light, water flow, substrate, wood, rock, plants), and the other fish species they are forced to share the tank with. If any of these factors are not what the species "expects," it will often lead to aggressive behaviour even from a normally "peaceful" species--like neons, cardinals, and frankly all the tetras, rasboras, etc, etc. A species that is known as somewhat aggressive to begin with--and here we have Serpae Tetras, Tiger Barbs, Black/White Widow Tetras, Emperor Tetras, Bloodfins and related species in the genus, and some others. These "known" fin nippers need special handling--larger groups, more space, and never placed in with sedate of long-fin fish.
You will note I do caution about neon tetras and all the other species. Provided they have what they need (the factors above), they should be peaceful. But the group must have around 10 minimum, regardless of the species. The more the better. A 2010 study of the effect of group size on angelfish, Tiger Barbs, white cloud mountain minnows, and neon tetras is instructive. Yes, neons were part of this study. The results confirmed what many of us have thought for some time...too small a group will cause aggressive behaviour within peaceful species or increased aggressive behaviour within the aggressive species. There were some other interesting findings too...darting, shoaling, and a distinct latency to feed were found to vary with group size in a species-specifific manner. In other words, the siz\e of the group has quite significant ramifications for the fish, even beyond aggression itself. The paper can be read (free) here:
Each species was divbided into three groups in separate tanks (obviously), in numbers of three, five and ten. The unquestionable benefit of ten was conclusive. With Tiger Barbs, the groups of three and five were removed from the study because the fish tore into each other almost as soon as they were introduced to the tanks, and the biologists considered it cruel to allow this to continue.