In character, Dekomori sees Rikka as her master (being a year younger), whilst Rikka sees Dekomori as her servant. The two of them are virtually inseparable and nearly always in tune; what affects one will affect the other. This extends beyond their respective chuuni identities. Dekomori genuinely cares for Rikka as a close friend, and though she has a bit of a selfish streak, it's evident that she would gladly make sacrifices for Rikka when presented with the opportunity. Despite this, Dekomori does have a degree of independence from Rikka, and she can effectively function as an anchor for her Master when Rikka falters. She will quickly take the side of anyone (even Nibutani, begrudgingly) who she sees as acting in Rikka's best interests, even if Rikka herself may not immediately agree.
Dekomori and Nibutani have an irritable, troublesome and sometimes even hostile relationship. While Nibutani was in middle school and acting as Mori Summer, Dekomori sought her advice through Internet forums, and held her in the highest esteem. When they meet in person, Nibutani is in full retreat from her former alter ego and admits to having burned the Mabinogion, something the "real" Mori Summer would never have done. Dekomori still loves and admires Mori Summer, but she stubbornly refuses to accept Nibutani's claim that they are the same person, instead forever branding her as a fake. Outwardly, Deko is contemptuous towards her because of this and establishes a rather nasty, almost sibling-like rivalry between them in and out of character, repeatedly sabotaging Nibutani's efforts to appear "normal." Underneath this contempt, the two of them hide a kind of respect and bond with each other. Deko almost surely knows deep down Nibutani IS Mori Summer and wants her to acknowledge this fully, though Nibutani likely never will again.
In the spinoff novel set in the future, Dekomori appears in a cameo as married to Nibutani. However, this may have been Yuuta having a bad dream since Dekomori still refuses to acknowledge that Nibutani was ever Mori Summer. It is left unclear by the end of the novel.
In character as Rikka's servant, Dekomori is almost always in lockstep with her, sharing many of the same opinions. She therefore has a deep reverence for the Dark Flame Master specifically, interacting with Yuuta overwhelmingly in that capacity and only rarely as himself (the end of S1E11 and beginning of S1E12 being notable exceptions). If the two of them and Rikka are interacting, Dekomori will follow Rikka's lead in how she treats Yuuta - except that because she does not have the same connection, she can be harsher towards him on Rikka's behalf when there's a conflict, taking more aggressive action where Rikka may be a little hesitant. Yuuta in turn sees Dekomori for the most part as a typical bratty chuuni and an underclassman to boot, but because of the connection to Rikka he remains friendly towards her and considers her part of his circle.
Dekomori encourages and accepts Kumin into her chuuni world, despite Kumin being two years older. Their interactions are friendly and pleasant, owing to Kumin's generally happy attitude and admiration of Deko's imagination.
Dekomori's interactions with Touka are few and always "in character". She knows Rikka's older sister only as the Priestess for much of the beginning of the series, and something of an enemy or foil for Rikka, so her opinion is rather contemptful of Touka. When they first interact at the Takanashi home over summer break in season 1, Dekomori learns firsthand over dinner why Rikka is terrified of her - Touka's patience with Rikka's chuunibyou is already strained to near-breaking, so she has absolutely none for Dekomori (plus Deko insults her cooking!!). From that point on, Dekomori considers her a powerful opponent not to be trifled with, showing her deference also for being her Master's sister, and even on occasion using this to try and gain favor to escape a bad situation (especially if she can throw Nibutani under the bus at the same time, as in S2E1). Touka, oddly, does not view Deko as a particular threat to her younger sister, though she must know Rikka's friend is not helping matters any.
Dekomori and Isshiki do not have anything of note between them, other than very brief conversations when the two are alone for plot reasons. Deko is completely apathetic towards him, for the most part. (She does, however, catch Isshiki's eye for the briefest of moments when she abandons her chuunibyou at the beginning of S1E12; but this being Isshiki, the moment she reverts, he suddenly loses all interest.)
And like the most of the protagonist she stops having interactions with
Dekomori and Shichimiya are equally devoted to their chuuni alter-egos, making their interactions free and easy. They are generally allies while in character and happily work with each other, despite Rikka's antagonistic attitude towards her in the beginning.