Most of Imperion's characters will live in, or at least spend some time in, the Dome. Even Outlanders were Dome citizens at some point. The Dome operates almost entirely independently of the rest of Tyrrhenia, and has its own culture and set up, thereby Outlanders have a different culture and upbringing than those that are raised in the Dome.
Climate
As the Dome was designed to be climate-controlled, weather patterns it experiences are very tame and predictable. Rain occurs occasionally, though it's actually more of a tank of water being released through certain sprinklers in the steel supports than actual rain. It isn't entirely known by the common person whether the sunlight that the Dome receives is actual sunlight, or just a very good mimicry of it, but it's most likely to be the latter. In the summer, the weather is warm and balmy, with just a bit of breeze and a decent balance between dry and humid. Most people with seasonal allergies do not experience them as intensely in the Dome, if at all, as there are natural allergen neutralisers in the air filters.
In winter, the weather cools off and artificially created snow is dropped occasionally. At times, this may turn into ice, but usually it's a fluffy, ski-worthy snowfall that doesn't pose any real trouble, and really occurs merely to keep to the season cycles that humans and the plant-life alike have come to expect. In higher altitude locations, it is usually several degrees colder than it is on sea level.
Commerce
For the most part, the Dome runs on an open market. As such, anyone is welcome to attempt to sell wares or provide services for a fee. There are business-class licenses and taxes that go along with establishing a company, but many can get away with marking themselves freelance to escape these fees. One good thing about being Unregistered is, there is no viable way for the Republic to enforce its licenses and taxes on Unregistered citizens, meaning a lot of small-time businesses and shops are run by Unregistered individuals.
The Dome uses the Cap as a currency. This works most similarly to the Japanese Yen in the real world. Thus, the prices on most things in Imperion's setting sounds particularly pricey to us, but it actually isn't. In example, an Omega COMP chip will cost around 100 Caps. This is only about 80 cents USD. Caps are called that because of the stamping machine used to print the images on the coins. This stamp leaves the edge of the coin in a shape that vaguely resembles a bottle cap, which first caused people to call them 'bottle caps,' and then later shorten it to just 'cap.' There are bank notes, but most of the currency traded on a regular basis is coins.
Indus is known to be the only city in the Dome that is openly and officially welcoming to Outlanders, primarily through effort of the Wintersky Outlander band. It is common for one to meet Outlander traders in Indus, but they are not entirely rare in other cities, either, barring perhaps Pyxis — the Outlanders like to pretend Pyxis and the Grid do not exist.
Culture
The Dome has an interesting combination of regional variance in cultural tradition, that changes between general area of the Dome one is raised in or most familiar with. Different regions within the Dome tout different speech mannerisms and accepted slang words, and have differing forms of art, religious observance, and holidays. In general, the closer to Eridanus the area is, the more refined and elegant these cultural trends will be, while the farther from it, the more seemingly random, wild, and rough they will be.
For instance, Eridanus and Aquila are known for their stone sculptors, whom create very well-crafted marble pieces depicting usually Demons or members of high society. Pyxis is more known for its vulgar graffiti, but while Pyxis' graffiti may seem crude and meaningless, it does tell an interesting story of hardship and the reality that many Unregistered citizens face in day to day life — a subject the stone sculptors of Eridanus and Aquila would know very little about.
Eridanus, Aquila, and Orion, have very formal religious observances. These are normally marked with a public gathering, honouring most likely some Asura or another, perhaps ancestors, and may include a banquet and some merry-making, but usually nothing too extravagant. Indus, Pavo, and Pyxis however, are very well-known for their week-long, rowdy, loud, and often entirely disorderly festivals for almost any reason they can think of. Indus, Pavo, and Pyxis, love to party, and they love to eat. … they also love a good excuse to blow things up — fireworks displays are very common during their festivals.
Education
Registered citizens are allowed the right to attend school. School levels somewhat vary, and are based on your intellectual abilities, rather than your age. Those that catch onto material quicker than their peers will progress through the school levels much faster than they. Typically, one eventually slows down, even if they may have sped through the lower levels relatively quickly. Teachers are given very small classrooms, and the environment is peaceful and focused. Students are expected to gain a basic grasp of linguistics, maths, science, technology, and history. Subjects beyond these will need to be studied independently, but there are plenty of decent tutors in subjects such as music and art.
One graduates from schooling when they complete at least 10 levels in all of the given subjects. Students may then go on to attend Aquila's Erebos University, which teaches more expanded and in-depth information on the basic subjects, as well as specialised courses in other things, such as sociology, psychology, Demons, arts, music, healthcare, childcare, and more.
Social Issues
There are several social norms that are held to in the Dome, and unfortunately, this does mean that sometimes, one is rather oppressed merely for being who they are. The most obvious will be that the Dome as a whole is rather homophobic and misogynist. Amusingly, the Republic itself is a lot more accepting of deviance from hetero-normativity, particularly in higher ranks, but the rest of the Dome can be rather offensive to gay people. If not outright persecuting them, and hate crimes against non-heterosexual individuals is quite common. It's also relatively common for gay people to find another gay person of the opposite sex to marry, just to keep eyes off them, if they are not very high ranking in the Republic.
Women are thought to be best suited to the home. Taking care of a household and any children in it is extremely important in the Dome, and it is thus relatively rare that a woman will attempt to pursue a career, especially one that does not deal with children in some way. However, like with homosexuals, women are much easier accepted, and better protected from prejudice, in higher rankings in the Republic, but some may still hold prejudices of some form against women, particularly if they are higher ranked than they are.
The Dome is in a pretty deep pit filled to the brim with controversy over the Psion Project, Demonicas themselves, and the war with Andasca. Some believe what the Republic says, that the Demonicas are necessary but dangerous, and Psionics are unpredictable snakes that can turn around and destroy them at any time. Others, however, are fiercely against the Psion Project's methods, believing it akin to slavery, and view the war with Andasca as a genocide. Plenty of fights and arguments have broken out over this opinion divergence.
Further, there is a small, but growing, opposition to the registration system, people that believe the registration system needs to be removed outright, and replaced with a public welfare programme that will assist unfortunate citizens in getting their feet under them. This opposition is most fiercely combated by nearly everyone in the Republic, as they believe it would negatively impact the Republic and its efficiency to bother.