These are the relationships of the Jade Princess and the Quiet One, Harumi.
Her Birth Parents
Harumi had a healthy relationship with her mother and father, whom she referred to as Mama and Papa. She loved them very much and lived happily with them until the Great Devourer attacked the city, which resulted in their apartment building being destroyed. Harumi's parents managed to save their daughter by pushing her into an elevator before they died when the building collapsed. This event had turned Harumi cold and had made her want revenge for their deaths. The only thing Harumi had left of her birth parents was a family photo, which she treasured and carried with her wherever she went.
In the book, "Garmadon Rulez!", it is revealed that after moving into the palace, Harumi kept their family photo in her journal. She wrote in the journal about how much she loved and missed them. Her birth parents, along with Garmadon, were the only people that Harumi didn't insult and she swore that even if Garmadon had adopted her she would always love them.
The Emperor and Empress had adopted Harumi sometime after her real parents died, making her the Princess of Ninjago, and raised her as their own. They hardly allowed her to leave the palace and were shown to be stern with her, as shown when they scolded her for befriending Lloyd since he was a Ninja and not royalty like them. Nevertheless, they loved and cared for her very much and didn't like to see her upset since the Emperor apologized for his harsh words after scolding Harumi and the Empress looked sad when Harumi ran away. Harumi appeared to love them as well and did what they asked of her. However, in truth, she didn't like being a princess and never saw them as her parents.
After the Emperor and Empress died Harumi had kept a photo of all three of them together along with the one of her birth parents and was briefly seen looking at it with sad eyes before she placed both pictures in the bulletin board where the Ninja kept their own photos of their loved ones. This showed that she may have cared for them, although this would also have been part of her act to make the Ninja believe she loved them so they wouldn't suspect she was responsible for their deaths.
Their relationship is further explored in the book "Garmadon Rulez!", where it is revealed that they found out about Harumi when she appeared in television shows and decided to adopt her. The Emperor and Empress enforced a strict education on Harumi to turn her into a princess the citizens of Ninjago would be proud of, expecting her to behave perfectly and follow the traditions of their family and in return, they supplied Harumi with any material good she wanted and needed but weren't very attentive of her emotional needs, as they believed that being made a princess should be enough for her to overcome her issues. When Harumi started behaving like the proper princess she was expected to be and became a model student, behaved perfectly and only spoke when spoken to as taught to her by the Empress her adoptive parents were very proud of her and foolishly believed that their daughter had resolved her issues.
Ever since she was a child, Harumi held no love or respect for her adoptive parents as she used to write in her journal about how much she hated them and defaced their photo. Harumi strongly believed that they adopted her as a publicity stunt and it is implied that there was no closeness or real parental love in the family, or that Harumi felt like they didn't love her.
Harumi served as the true leader of the Sons of Garmadon. She had her orders relayed to the lower-ranked members by her three generals, Mr. E, Killow and Ultra Violet. The S.O.G were seen to look up to her and at times fear her, Ultra Violet, instantly turning tame upon hearing her voice on the other end of the phone and Killow warning one of the bikers that the Quiet One was sure to do far worse to him if he wimped out of entering Primeval's Eye. It's possible some lower-ranked members had never met her, but most of the S.O.G seemed to know her identity as the Jade Princess, Harumi. Harumi did seem to care for them in some way, as she prevented Lloyd from attacking a group of them while they were bullying children, and the first thing she did after escaping was rush to free them. She also had entrusted the Oni Mask of Hatred to Ultra Violet, showing she believed her to be a capable general. Killow and Violet even took amusement in watching Harumi mock a heart-broken Lloyd, as well as sharing a laugh with Harumi at Garmadon thrashing Lloyd.
She seemed to value her comrades as she was terrified when Garmadon destroyed Mr. E and even begged him not to do it but to no avail and she was horrified at his destruction.
Although Harumi cared about the S.O.G. it is implied that they didn't care back as shown when Killow and Ultra Violet blamed Harumi for failing to prevent the Resistance from taking over Borg Tower to deliver a message to Ninjago and escape, knowing that Garmadon would try to kill her. Ultra Violet also seems to be jealous of Harumi, due to Garmadon's favoritism towards her. Yet they watched on with shock when Garmadon attempted to do just that, implying they do care for her but were just scared to face the same fate. It is unknown what their reaction was to her death.
Harumi worshiped Garmadon from the day she found out he had saved the city from The Great Devourer, not the Ninja. This led her to believe he was the hero and wanted revenge on the Ninja. She resurrected Garmadon as a soulless and heartless monster, to use him as revenge on the Ninja, especially on his son Lloyd. She enjoyed showing off his power and the fact he was reborn. Harumi aided him in taking over the city and keeping the Ninja from interfering with his plans.
After Garmadon subjugated the city in Season 9, Harumi worked closely with and became an advisor to him. In "Firstbourne," she suggested sending Mr. E to procure Lloyd rather than letting Garmadon destroy their territory. Garmadon appeared to value her input as he agreed with her suggestion.
However, in "Iron & Stone," Garmadon was angered by Mr. E's failure and Harumi was scared as he destroyed the Nindroid in front of her. Garmadon turned his attention to her, he threatened to do the same to her should she fail him as her colleague did. She was terrified and complied with his order. However, despite his threats she still viewed him as a leader and superior and was always trying to please him.
In "How to Build a Dragon," Garmadon was yet again angered by Harumi's failure and almost killed her, yet she still remained loyal despite screaming in fright.
In "Two Lies, One Truth," Garmadon proclaimed Harumi to be his new daughter.
During "Saving Faith," she stood by Garmadon’s side during his fight to control the Colossus. Later she warned Garmadon to leave, but he refused. Fearing that he would fail and they would die, she ran away, abandoning him and ran down the steps from Borg Tower, using a zip line to another building. Harumi then had a change of heart, this being shown when she saved a little boy and his parents. This situation was similar to the incident with the Great Devourer. Harumi then leads them to safety and she was standing on a building that was about to be destroyed. Garmadon noticed her escape and was worried for her safety before the building was destroyed. When Harumi died, Garmadon cried out in genuine fury and sorrow, and turned his rage towards Lloyd, wanting to make him pay.
Lloyd had a crush on Harumi from the moment he saw her. Harumi quickly realized this and began growing closer to him, allowing him to call her "Rumi" instead of "Princess" as the other Ninja had to. Harumi appeared to like Lloyd back, even trying to kiss him, before he made an excuse and quickly left.
In "The Quiet One" she told him she had always dreamed of being with him, and even kissed him on the cheek, later on, making her Lloyd's first kiss. However, all of her care for him was apparently a ruse, just to lure Lloyd in to make him and the Ninja trust her to get the Mask as she hated the Ninja for failing to stop the Devourer and she especially hated Lloyd since she knew he was responsible for the incident since it was him who released the Serpentine. In "Game of Masks," she revealed her plans to Lloyd and they fought, now enemies. Lloyd was defeated when Harumi used the Oni Mask of Hatred and Lloyd was captured.
In "Dread on Arrival," Harumi mocked Lloyd for ever falling for her, telling him that there was really never anything between them, revealing that Harumi apparently never liked Lloyd back, thus breaking Lloyd's heart. She went as far as mocking and putting both him and his mother in a dangerous situation. After she was defeated and arrested, she pleaded with Lloyd by telling him that he was right and she wasn't herself in her attempt to resurrect Garmadon. Lloyd didn't buy it and coldly slammed the door in her face as she tried to charge at him.
She later faced him again in "Big Trouble, Little Ninjago," where she demanded he hands over the infant Wu and Lloyd told her she is just repeating the Devourer in attacking the city but Harumi ignored him and chased him through the city. After cornering him, she asked him to join her, a contrast to her attempts to kill him. However, he refused and after Lloyd was able to give Wu to the Ninja, he briefly fought with Harumi, although he wasn't too rough with her as seen when he twisted her arms behind her back instead of hitting her. Harumi held Lloyd by the throat and made him watch as the Ninja were "killed" by the Colossus but this time she didn't try to kill him (even though she had the chance). Instead, she put him down on the top of the tram carefully, which suggests that she may have actually liked him enough to not kill him. However, she was angry by his escape and screamed in fury.
In "Firstbourne," when she reported to Garmadon that Lloyd still hadn't been caught, she was opposed to his plan to use the Colossus to draw him out and suggested sending Mr. E instead.
During "Radio Free Ninjago," when Lloyd made his speech to Ninjago of rebelling, Harumi was angry to see him again and tried using a recording of his loss against his father to stop him. Her attempts had nearly succeeded but he overcame it and continued speaking. She and Killow barged in, only to find them gone. She was furious at his escape but realized the location of their base after seeing garbage trucks driving away.
During "How to Build a Dragon," Harumi was nearly killed by Garmadon but saved herself by revealing the location of Lloyd and the resistance. This also hints that she might have liked him as she did not report to Garmadon about the hideout immediately.
In "The Gilded Path," she faced Lloyd again and he was shocked to see her before she overwhelmed him in battle but he was saved by his friends and escaped her grasp.
In "Two Lies, One Truth," she met him again while she was confident in defeating him, she was dismayed to see he had tricked her and she ended up captured by Lloyd and the rest of the resistance.
During "Saving Faith," she saw Lloyd watching her trying to escape the Colossus and they shared a gaze at each other. Harumi's facial appearance seemed to mean that she had now understood his words about having someone endure the same fate she had before she died trying to save the life of a boy and his parents. Lloyd had a concerned stare on his face, as he faintly said her name.
As a young child, Harumi was a fan of the Ninja including Nya when she was still Samurai X after she saved Harumi's village from the Skulkin until the day the Great Devourer attacked and destroyed part of the city including the apartment complex where Harumi lived with her family, resulting in the death of Harumi's parents. While sitting in an ambulance Harumi heard from the paramedics that Garmadon was the one who had killed the Great Devourer and had saved the city, which led to Harumi believing Garmadon to be the real hero and to hate the Ninja for being careless with the city, during their battles as well as failing to save her parents. Harumi then spent the following years plotting her revenge.
Harumi later died without knowing the ninja survived and couldn't witness them saving Ninjago and defeating Garmadon.
Hutchins was Harumi's bodyguard during her life at the Royal Palace. She appeared to trust and respect him, treating him like a second father. Hutchins did his best to protect her and Harumi did as Hutchins asked. In reality, she did not care for him at all, giving the orders to attack the Palace with resulted in her adoptive parents and Hutchins' deaths.
Their relationship is further explored in the book "Garmadon Rulez!", where it is revealed that Harumi despised Hutchins ever since she was a child and ignored him when he suggested she talked about her problems, believing him to be nothing but an old man who just did what the Emperor and Empress told him to do and knew nothing about feelings. Hutchins did care about her and did things like reminding her to brush her teeth and, unlike the Emperor and Empress, was aware of Harumi's emotional issues and gave her a journal so she could write about her feelings, telling her that it may help her. Harumi did as he said and wrote about her feelings in the journal but it did not help. It was Hutchins who taught Harumi the lullaby "Spider Bit The Mouse" and used to sing it to her when she couldn't sleep although she as a child found the song to be creepy. It is also implied that he may have grown suspicious of her and what she was really doing, which drove Harumi to have him killed as well.