Powers
Demon Physiology: Mazikeen is superior to humans, having supernatural powers. She is also considerably stronger than other demons, however, she is not as powerful as Angels.
Immortality: As a demon, Mazikeen doesn't age and has lived for thousands of years. Lucifer even explained that life in prison would be a mere timeout for her. However, demons do not have souls, so if she dies, she would be eradicated from existence. It is unclear though whether or not she can be killed, like other demons, by extremely mundane means, as she has never displayed any fear of mundane weaponry, indicating she is far more durable than the common demon, a fact further supported by the fact she can take punches from Lucifer without much problem, while other demons were taken down by one punch of his. She cannot die of old age.
Superhuman Durability: Mazikeen is far more durable than humans. Mazikeen can withstand an immense amount of physical damage, and weapons such as guns, knives, and tasers cause her little to no harm. Usually, Mazikeen laughs at the idea that humans may hurt her, and after a punching duel with Lucifer, she was only moderately injured (while a single light punch of him is enough to knock a human unconscious and severely injure them), and could still walk, although it turns out that Lucifer was holding back a lot and despite being able to recover reasonably quickly from being palmed by him, another such attack, with Lucifer deciding to hurt her enough, effectively incapacitated her.
Accelerated Healing Factor: Mazikeen have shown to heal faster than humans, though still slower than angels. After her fight with Lucifer, she was shown to be already in a somewhat better condition after only several hours, however still in a worse condition than Lucifer.
Superhuman Strength: Like all Demons, Mazikeen is much stronger than humans and animals. She can easily knock a human unconscious with a punch and she can lift large men by their necks very high off the ground with only one hand, and shove them into a wall, she can break out of handcuffs with no effort, and she can single-handedly annihilate 12 large men in combat. While weaker than angels, she can still punch them hard enough to make them draw blood.
Superhuman Speed: Mazikeen can move far faster than humans and animals. In less than a minute, she went from being outside Linda's office to in her office which required her to leave the building and go through the window. Mazikeen single-handedly destroyed a street gang in about a minute.
Superhuman Reflexes/Reactions: Far greater reflexes than humans.
Superhuman Agility: Supernaturally agile, and is able to move incredibly quickly and easily.
Superhuman Senses: She has better senses than humans and animals. She also appears to have better senses than angels, as, multiple times, she was able to detect things Lucifer hasn't noticed.
Superhuman Intelligence: Mazikeen is naturally more intelligent than the common humans, as witnessed she is capable of quickly understanding even situations she has never handled before. She also has a vast amount of knowledge, due to her age.
Shape-shifting: Mazikeen is able to change her appearance into a form she refers to as the Demonic Left Side of her Face. That form varies along the seasons. In Seasons 1-2, it manifests as a mutilated, monstrous, and scarred-looking version of her appearance. In "Sweet Kicks", Mazikeen reveals her demonic face in a mirror when Chloe Decker was asleep. S02E06, during Halloween, Maze shows her demonic face to Trixie. Like all demons, Maze can change her form, although only if demons are inside hell loops.
Telekinesis: Mazikeen was able to summon her knife from a wall into her hand in order to fight Amenadiel. However, it is unknown if she can utilize this ability on any other object.
Demonic Growling and Roaring: Like all Demons, Mazikeen has supersonic growling and roaring, she can growl and roar fiercely and very loudly, similar to animals such as lions, bears, and tigers. To frighten a misbehaving child Maze perfectly imitated the sound of a vicious dog barking and growling.
Demonic Possession: As a Demon, Maze can possess any recently deceased human being. Lucifer has forbidden Demonic Possessions because "someone" in the Silver City complained about it.
Spirit Communication: Mazikeen can communicate with ghosts, like she did with Dan Espinoza after his soul was released from Hell on Earth.
Abilities
Expert Hand-to-Hand Combatant: Mazikeen has shown to be an expert in various types of martial arts. She is a highly-skilled fighter and has shown to have brilliant armed and unarmed fighting skills. Her fighting capabilities are shown to rival Angels despite her inferior status as a Demon which is clearly evident through her multiple scuffles with Amenadiel, Uriel, Michael, and Lucifer himself. However, the series makes it clear that she isn't a better fighter nor as powerful as these Angels as she's shown to be effortlessly overpowered and incapacitated by a serious Lucifer in Season 5 as well as Uriel in Season 2. Although she was able to surprise Michael and cause him to "submit" with one of her fierce grapples, it is unlikely that Michael was being serious since he later subdued her in a matter of seconds. Maze can be very precise and surgical in her attacks, as noted by Lucifer when she targeted her opponents' weak spots, notably shattering a tibia, causing an orbital fracture, and crushing a humerus in "Sweet Kicks".
Superhuman Athleticism: As a Demon, Mazikeen is in far better shape and a far greater athlete than the finest athletes on earth. She is an expert martial artist and a master in karate, boxing, muay thai, jiu Jitsu, kungfu, aikido, wrestling, judo, taekwondo, ninjutsu, eskrima, etc. She has the superhuman abilities to easily and effortlessly defeat multiple humans.
Expert Stick Fighter: While in a bar fight Maze broke a wooden pool stick into two pieces and easily used them to defeat a large group of attacking men.
Expert Knife Combatant: Mazikeen has shown incredible fighting skill with demon knives when she fought Amenadiel, though she was still ultimately unable to defeat the angel. She was also capable of holding her own against Uriel for some time before she was deprived of her knives. When fighting Lucifer with her knives, Maze was able to temporarily pressure the reluctant Lucifer but was easily defeated when he had enough.
Persuasion: To a small degree, Mazikeen can convince people to make a decision that they think is their own.
Expert Masseuse: Since Mazikeen can find most of the pain points in a human's body, she can also relieve the tension in them, making her a great masseuse.
Expert Tracker: Mazikeen is an expert tracker, which is why Lucifer first brought her to Earth from Hell to help him track down the one who stole Amenadiel's necklace. This is also the reason why she is so successful at her bounty-hunting job.
Bilingualism: Maze speaks her native Lilim in addition to fluent English, as seen in "Everything's Okay" and in "A Chance at a Happy Ending". But in reality, it's a derivative of the Afrikaans language.
Weaknesses
Celestial Beings: Despite being a very powerful demon, Mazikeen has proven herself to be outclassed by Angels. Amenadiel, Lucifer, and Uriel have all proven themselves capable of defeating Maze. Once Lucifer stopped holding back and actually wanted to harm Maze, he was able to not only powerfully knock her down and stun her with a single light palm blow but the next time he did that, he incapacitated her. Even in a weakened state, Goddess was able to knock her out with a headbutt. Amenadiel was able to overpower Mazikeen in hand-to-hand combat.
Gods: God and Goddess can effortlessly kill and eradicate Mazikeen and any other demon from existence.
Flaming Sword: The Flaming Sword can instantly eradicate Mazikeen from existence.
Demon Daggers Forged In Hell: These daggers can easily kill her.
Abandonment issues
After the birth of Amenadiel and Linda's child, Charlie, Maze begins experiencing abandonment issues from her own mother, the first demon Lilith. Maze is able to bargain with Trixie to ask Lucifer for the history/story surrounding her mother, and when Trixie repeats the story to her, Maze seeks her mother out. Maze finds that her mother abandoned her — and the other demons — because she believed she could give them a better life.
Maze's abandonment issues cause issues in her relationship with Linda when the two clashes over Linda abandoning her daughter when she was seventeen. Maze is eventually able to see, however, that Linda too believed that giving up her child was the only way to give her a better life.