Chitoge and Seishiro share a very special relationship backed up by their respective childhoods. Aside from Raku, Seishiro was once a frequent playmate and friend to Chitoge. Seishiro greatly treasures her time with Chitoge, owing to her her happiness and all the precious memories of her despite being unaware of her own true origins; Chitoge was the one who gave Seishiro the date of her birthday - the day they first met - and also provided Seishiro her signature light-blue ribbon. Because of this, Seishiro developed strong feelings of love and dedication to Chitoge, pledging to become strong enough to protect her. Hence, Seishiro trained herself and rose to become one of Beehive's most effective agents.
'Till the day they reunited again as teenagers, Seishiro was psyched to see her old friend once again that she pounced at Chitoge. Her love and dedication to her unwaivered and was willing enough to eradicate anyone who dares to interfere. This led to her initial confrontation with Raku, whom Seishiro had orders from her handler, Claude, to annihilate out of pure distrust. Eventully, Seishiro came in terms with Raku, albeit with some caveats.
Despite being Chitoge's personal bodyguard working for the Beehive faction, Seishiro still goes out her way to interact with Chitoge as a close friend as she only acts to do anything that would benefit her own happiness and would go out her way to disregard strict orders, even from her higher-ups, just to keep Chitoge out of harm's way. This is examplified when Seishiro raised her own weapon against Claude when she was in disgreement in forcing Chitoge to move back to America.
Generally, Seishiro sees Chitoge as an invaluable and irreplaceable friend, one whom she is willing to throw away her own personal feelings for someone else and instead dedicate herself for Chitoge's own safety and happiness. Even despite knowing Chitoge and Raku's fake relationship, Seishiro nonetheless continues to view Chitoge the same way as she came to understand her situation and the consequences she has to face as to why she had to act out her relationship with Raku.
Seishiro and Raku had a rough first encounter when Claude had Seishiro Raku to be annihilated. Eventually, after their duel where Seishiro lost, she and Raku came in terms with one another. This, however, led her to grow infatuated with the young man, as Seishiro came to acknowledge Raku's general kindness and restlessness to others. As such her interaction with Raku usually has her feeling uncomfortable and jittery, to the point that she instinctively raises her voice against him in an effort to distance herself from him. Seishiro's feelings for Raku is shown in volumes when Seishiro pushed herself to embrace Raku thinking it was the effect of a love potion she accidentally drank earlier when in truth it was not and that the effects of the potion have long subsided.
Paula is the only one to notice Seishiro's feelings for Raku and, in turn, encourages her to pursue him, much to Seishiro's discomfort.
However, since her relationship with Chitoge outweighs that of her feelings for Raku, Seishiro constantly convinces herself to move on with her crush with Raku and focus on serving her best friend/master with little to no results. Seishiro also keeps a close eye on Raku for any activity that would jeopradize his relationship with Chitoge and gets jealous and enraged whenever a girl - Marika, for the most part - flirts with Raku, reprimanding her under the pretense that he is in a relationship with her master.
After knowing that Raku and Chitoge's relationship was a ruse, confirming her own feelings and that of Chitoge's, Seishiro finally confesses to Raku vocally in tears albeit covering Raku's hearing in the process. Through this, Seishiro is finally dedicated to live out her life to serve her beloved master.
While not shown as close friends, Kosaki and Tsugumi share a mutual friendship and are seen to be together at times, usually with Chitoge, particularly at sweet shops. Unbeknownst to Seishiro, they share on having a romantic crush at Raku.
Seishiro is often times seen reprimanding Marika for flirting around Raku, masking her jealousy by stating that it is inappropriate and the fact that Raku is already in a relationship with Chitoge. Aside from this, however, Seishiro also sees Marika as a friend.
Seishiro usually sees Shu and his antics as annoying and detestable, and is often times seen beating him. Though it is also implied that he may be aware of Seishiro's feelings towards Raku.
Both being hitwomen, Seishiro and Paula see one another as comrades and respect each other's skill set. While Paula admires Seishiro and her reputation as a very skilled, albeit feared, agent of the Beehive gang, Seishiro looks out for Paula's well-being, advising her to be socially active and not only being solely focused on training herself and on missions. In turn, Paula, being one of the few people aware of Seishiro's feelings towards Raku, constantly teases and encourages Seishiro to give in to her emotions and pursue Raku, much to her chagrin.
In a way, Seishiro acts as a doting big sister for Paula, a view also shared by Paula towards Seishiro as said by Haru. -.-