Demons

Chosen souls
The first and most common way for a demon to come into existence is if a sinner dies and Luci takes a liking to them and offers them power. They then go through the first trial and upon success, become a demon.

If a person's sins are so grave that lucifer feels the first trial isn't enough to 'purify’ them, he may force them to take multiple trials in a row before granting them power- Upon success they'll become particularly strong demons. In the case a living soul enters hell, they are automatically chosen to become a demon. That’s because their own life force becomes a source of their power- something that makes them extra valuable for lucifer. For a living being, stepping through the gates is the same as giving Lucifer their soul. Should they refuse the trial or fail it, they simply die and become a regular soul resident of hell.

Chosen souls cannot reproduce with another demon. However, they can reproduce  with the living which results in the birth of a half demon.

Living demons
Another, much rarer, way for one to become a demon is when a living being is turned. For this to work it requires an especially talented demon to carry out the transformation, and a natural affinity for demonic power from the side of the living being. The living being doesn’t have to be human, they can be anyone from the mortal multiverse. A person transformed this way doesn’t have to give up their memories and also retains a physical body, allowing them to remain in the physical world if they chose to.
 * It should be noted that while these kind of demons are the 2nd strongest after the direct descendants, they have a limit to how much power they can draw from Lucifer. They can only take trials in order to develop their power up to the circle their soul would have belonged in, had they died naturally. Because of this, only those who have committed serious treachery can make it to the 10th circle and become guardians.

Direct Descendants
The third group of demons, referred to as Direct Descendants, is a bit different. In truth, rather than demons they should be seen as infernal demigods. As their name suggests, they are the descendants of Lucifer: Lucifer's children, grandchildren, and so on. Their family has an interesting and wide range of characteristics, some of which may seem far from demonic.

Fallen Angels
Like the above, Fallen angels aren’t actually demons. They are angels who lost their place with ‘god’ and were banned from heaven. Fallen angels are generally banned to the mortal realm, so they don’t actually need to live in hell. However, some choose to ally themselves with Lucifer and reside in hell anyways, standing against the selfish god who lost their trust.

Half demons
The result of a demon and a living being cooking up a baby. Half demons normally don't live in hell, or even have anything to do with it. They are always raised by their living parent, since new souls cannot be born in hell, with the exception of those related to Lucifer.

Half demons are powerful for the same reason living demons are- they own their own soul and have their own life energy, which means they don't have to steal any from others, unless they use their demon powers too much. A lot of half demons don't even know what they are, since the living parent who raised them tend not to know the truth themselves.

Lucifer
What we know about Lucifer is this; They can freely change their sex, gender and form. Within hell, they're a completely omnipotent being. They have many children with various entities, and one of those is Ceyx- the son of Lucifer and River. Lucifer is not a demon, but rather a fallen angel. A Seraphim to be exact.

Outside of hell, Lucifer is not omnipotent, but their exact range of power is unknown. Lucifer draws their power from the souls in hell. The more souls there are the more powerful they are- but the power of regular demons is also derived from Lucifer. Should they choose to, Lucifer can take that power back to strengthen themself, and temporarily leave their demons powerless. Because of this it's virtually impossible for demons to oppose them. Living demons and Direct descendents are an exception to this rule, as they have their own power as well.

In relation to the Loveshack- Lucifer did not intentionally create the Loveshack, but rather agreed to an idea quipped to his son Ceyx by another demon. How exactly they view the shack is unknown, but it’s very likely a mere source of entertainment.

Demon abilities
There’s such a wide variety it’ll be close to impossible to describe, but there are limits. For one, demon powers are ultimately powers granted by Lucifer- Which means they can never excell Lucifer's power.

Demons draw power from life energy, which means the more they have, the stronger they are, and using their powers consumes life energy, therefore it makes them weaker. All demons, no matter how small or weak can steal life energy from living creatures. Their methods vary, as does the amount and the speed at which they can consume.

Demon powers are never absolute- they cancel eachother out when the opponent uses the same power, and their effect varies depending on their opponents strength- particularly mental strength. Smart, calculated opponents are typically more difficult for demons, as they are able to partially resist some of their most prominent powers; namely, powers that affect the opponent’s perception. Common demon powers are those that affect the way the mind perceives their surroundings. From subtle changes affecting their mood, to full blown hallucinations.

That said, demons can have physical powers too. Higher strength and speed and toughness for their size are the most common among those- long term flying and poison are less common but can still be considered normal, while elemental powers are extremely rare and generally only found among demons in the highest circles.

Demons that have passed the 7th trial receive what's knows as the 'inner fire'. This so called fire helps them defend against the elements and gives them the ability to directly absorb energy in the form of heat or electricity. The inner fire protects them from taking fire damage, but also defends against ice attacks through melting, water attacks through cooking, and it's able to crack earth if it encompasses the demon.

Talented Demons can learn powers unrelated to their demon nature, but those powers cannot become stronger through taking the trials.