While parahumans were based on humans and spliced with cosmetic genes from a variety of different animal species, there are a few traits that are common to the majority of the parahuman population that differentiate them from humans.
Cardiomuscular: Perhaps the most notable change the corporate geneticists made was the increase in hemoglobin and myoglobin levels to the point where their blood and muscle tissue almost appear to be black in color. This greatly increases their oxygen retention capacity with minimal increase in internal air pressure, enabling them to remain conscious in vacuum for up to ten minutes, after that they go into a torpor in which they can survive for another hour without air.
The geneticists of Alpha Centauri, both factions, were able to maintain this trait throughout the centuries. But in Tau Ceti and Epsilon Eridani many parahumans lost much of their -globins through mutations. Some from those systems refer to Centaurans derogatorily as "blackbloods".
Dietary: Their iron-rich blood requires an iron-rich diet. Almost as important as the development of the parahumans themselves was the development of a series of high-iron legume and algae that could be grown on ground-up asteroid. In modern Federation society this isn't much of a problem, those GM crops and vat-grown or nanofabricated meat is readily available. However, it does help explain why many Cetans and Outworlders lose their high hemoglobin levels, and it's one of the reasons why ghuls are obligate cannibals.
Skeletal: While the skeletal structure was changed to accommodate body parts like muzzles, ears, and tails; the baseline skeletal makeup is barely different. While the first generation were bioprinted with titanium-reinforced bones, the complete lack of biological interaction exhibited by the metal made it impossible to code the trait into the genome. However, many parahumans, especially spacers and military, use microbots to reinforce their skeletons as adults.
Environmental Tolerances: Parahumans can tolerate a lower range of oxygen partial pressures than humans due to their blood. However, they experience oxygen toxicity at a lower partial pressure than humans would, which would still be substantially higher than Old Earth's when it was last inhabited.
The presence of fur helps insulate parahumans but makes higher temperatures unbearable, especially as they lack sweat glands. Between 20 and 35 degrees Celsius the average parahuman tends to wear minimal clothes, in many places where such temperatures are common nudity is acceptable, especially for polar species. When parahumans need to spend extended periods of time at 40 C or higher they make use of ventilated suits with coolant pipes.
See also: The environment suits worn by the uplift mission to the kershkans in A World Lost.
Torpor: As mentioned above under "Cardiomuscular", parahumans can enter a deep torpor or hibernation when deprived of oxygen. The idea was that a transport filled with parahumans kept unconscious at a low oxygen level would save on life support costs until they arrived at a station. However, they still age while in torpor so it's only useful for intra-system or gate travel. Combined with microbots, however, a parahuman could spend centuries in a torpor, or remain alive as a severed head even.