–Intro—To start with, the term “bat-pony” isn’t technically accurate at all from a biological perspective. Genetically, they’re just pegasi; it just happens that pegasi have a variety of possible traits they can inherit.
 
Those who is currently considered to be “bat-ponies”, are actually just pegasi with a combination of several different, unrelated, traits. Some of these -the ear tufts and the naked ears are actually not limited to pegasi at all, and all ponies can inherit them. However, the “cat-eyes”, fangs and bat-structured wings are tied to the genetics which determines if a pony is a pegasi, unicorn or earth pony. Unless there are some other mutations in play, no earth ponies or unicorns have slitted pupils or fangs.
 
–Biology–  
Most Chiropterasi have bat-like wings, with a clawed thumb and three long “fingers” connected via leathery skin membranes. The “arm” of the wing is usually covered in extremely short and fine fur, while the membranes are naked. This causes the wing to usually be a different color than the rest of the pony, as the color of the skin of the pony doesn’t always match their fur color.
 
Luckily, the bone structure of a pegasus’ wings seems to be one or the other either bat-structured or bird-structured, nothing in-between; if that ever were to happen, it would be very unclear if the pony in question would be able to fly or even comfortably fold their wings, hence the “luckily”. What can occasinally happen is a pony with bat-wings having feathers or someone with bird-wing being covered in short fur. The former is not terribly uncommon, and may cause the pony some issuses with flying initially but isn’t severe in the long run. The latter is a lot rarer and will make the pony to be completely unable to fly without some kind of prothetics.
 
The eyes with slitted pupils are better at seeing in low-light environment than those with round pupils; although, similarly to those with round pupils, they mainly see in grey-scale when the amount of light is low. They are much more sensitive to light, and those who have to be awake and outside during the day can often be seen wearing sun-glasses, even during overcast weather. While not always true, the sclera is often slightly colored.
 
Despite them often being referred to as “bat-ponies”, they aren’t actually bats. They cannot sleep upside down anymore than a normal pegasus can. Any who tries just faints and then get concussions.
 
 
—Culture–  
The country of the Chriopterasi is still (suprisingly?) a democracy. When it was first founded, the original inhabitants had just left a heavily rigid and military based society, of which they were generally considered outcasts, so they were very keen on personal freedom and anti-authority. At the beginning, they were few enough in numbers that having everyone vote on major decisions was actually feasible; whoever had a proposal would send out a message with a date and time, and those who wished to vote would gather in a coliseum-like structure. Anyone who wished could take the podium and argue their position, and once everyone had said their piece, the vote was held.
 
This system was fairly slow, so when the country was reformed with a lot more inhabitants, they opted for a representative democracy. Each “county” votes on local matters, and selects a representative who votes in national matters. Nation-wide votes are still held for really important decisions, such as when they opted to open their borders to Equestria.
 
Socially, they live much more like larger closer groups than ponies do, while also much more isolated -while ponies traditionally live with their closest family in a tight-knit settlement, chriopterasi usually live together with their extended family but more spread out from other family groups. This isn’t always true, as there are several larger cities, but it is the norm for the majority of the country. The reason nowadays is just tradition, but the original reasoning was that hunting in larger groups were easier, but you could not have too many living too close to each other or you’d overhunt the area. But nowadays, as most of their meat is produced by farms and such, they don’t really hunt wild game all that much.
 
Equestrain chriopterasi are varied in their social structure; some still live with their extended family a bit outside of pony settlements, and some have adopted the smaller family units and live in the settlements. It usually depends on the pony and their reason for moving to equestria.