Author's Note-My own headcanons about merfolk biology and society is a blend of my own ideas, Disney's The Little Mermaid franchise, the Filipino telenovela series "Dyesebel", Hans Christian Anderson, and some ideas I've incorporated from other FictionPress series such as "Human To Fish" by Fantasy Ocean so I must give some credit to some of my inspirations.
Merfolk biology is quite unique, complex, and fascinating, as despite physically resembling half-human, half-fish hybrids, they are actually very special and magical aquatic creatures that have evolved over millions of years to function in ways that vaguely resembles certain species of reptiles, amphibians, and fish, but is in fact quite different from just about any other known living being.
Merfolk come in various shapes and sizes, with every eye, skin, and tail color imaginable, and can live for as long as a thousand years and generally physically stop aging in their mid-thirties. When a mermaid or merman dies, their bodies transform into sea foam. Because of that, "foaming" is a commonly used synonym for death among them.
They are able to breathe underwater through tiny gill slits on the back of the necks, which is usually covered by their long, thick, luxurious hair. If they are out of the water for a number of hours, they can die from dehydration, and some merfolk have a higher tolerance to dryness than others. Chlorinated water is very difficult for them to breathe.
When a mermaid or merman cries, their tears fall to the sandy bottom of the ocean floor, where they sometimes turn into colored pearls. Pink pearls are tears of joy, yellow pearls are tears of sorrow, and blue pearls are tears of fear.
A mertail is arguably more elegant in appearance than any fish or marine mammal's fins. It begins right below their belly button, and is blanketed in delicate, colorful scales that shimmer in light. Instead of a single, broad tailfin like so many aquatic animals posses, their long appendange ends in a pair of semi-translucent flukes which appear almost too silky and billowing to be adequately hydrodynamic, but they are capable of swimming up to eighty miles per hour, holding their arms primarily to their sides and letting their flukes propel them forward in feathery, dolphin-like movements. Their vaguely ribbed texture suggests there is some kind of bone and vein structure inside.
The color of a mermaid or merman's tail is said to coincide with their personality. Merfolk with red tails are supposed to be energetic, confident, passionate, courageous, and strong, and their worst can be aggresstive, rebellious, obstinate, impulsive, and egotistical. Orange-tailed merfolk are said to be sociable, optimistic, enthusiastic, and cheerful, but can also be superficial, insincere, over-bearing, and self-indulgent. At their best, green-tailed mermaids and mermen are self-reliant, dependable, tactful, and compassionate, but they are also capable of being possessive, materialistic, over-cautious, and envious. Merfolk with blue tails are loyal, trustworthy, responsible, and peaceful as well as rigid, self-righteous, weak, and unforgiving. Purple-tailed merfolk are said to be very creative, intuitive, dignified, charismastic, and generous, but also can be immature, impractical, aloof, pompous, and highly eccentric. Mermaids and mermen with pink tails are often romantic, loving, warm, hopeful, and sweet at their best and naive, over-emotional, needy, prone to unrealistic expectations, and lacking in willpower and self-worth at their worst. A silver-tailed mermaid or merman is supposed to be soothing, glamorous, insightful, sophisticated, and gracious on good days and melancholy, indecisive, deceptive, moody, and snobbish on bad days. Gold-tailed merfolk generally have a good sense of self-worth and are incredibly popular with others, but can also be self-centered, demanding, mean-spirited, distrustful, and greedy. Merfolk with white tails are associated with innocence, purity, and fairness, but can also be overly cautious and critical. Black-tailed mermaids and mermen are said to be sophisticated, seductive, mysterious, independent, and determined, but can also be aloof, pessimistic, secretive, overly serious, and intimidating.
One of the most unique biological features of merfolk is the nature of their digestive system. Their spleen is on the opposite side of their body as humans, and their stomachs are much larger than a human's as it contains six chambers that allow them to digest food much more completely. They also lack a large intestine because merfolk do not eliminate metabolic waste from their bodies the same way that humans and just about all other non-magical beings, including many of their fellow sea creatures do. Instead, they odorlessly secrete excess nutrients through their scales, almost like sweating. This is basically invisible to the naked eye, but if one put the water around a mermaid or merman into a microscope, they might see bacteria and such.
Since part of why their digestive system is so efficient is that it has evolved to eat only a very specific diet, which is mostly plant-based but occasionally supplemented by small mollusks such as clams, oysters, and mussels for protein, they are however capable of vomiting when eating unfamiliar foods. Large crustaceans such as crabs and lobsters and especially all kinds of finfish, however, are not eaten by them because not only are many merfolk able to communicate with them and thus consider them something close to equals, but their stomach would be able unable to process them.
As for the age-old question as to how do merfolk reproduce...well, that remains a complete and utter mystery to this day, although it is relevant to note that they obviously do indeed have mammalian breasts and belly buttons.