Looking at it strictly narratively speaking for a second, a part of me doesn't read into why she was following her around too much because really the scene is Uika's biggest non-post-credits scene. They couldn't just leave it at the planetarium without following it up with something more.

I kind of interpret it as she used the seat issue to get Tomori to acknowledge her (since we all know she obviously knows how the seats work), which based on the fact she thinks about Crychic when they're sitting together, is probably because she recognized her as Sakiko's friend. She noticed something about Tomori seemed off so she kept an eye on her as she left. I don't read anything in this or in her conversation to her as malicious; while I know the series trusts us to read in between the gaps, I do think they would be more deliberate if they wanted us to leave that scene thinking "Uika is a freak."

As for the conversation itself, my interpretation of it is the "Even in the city, you can see the North Star... so I was surprised that I found it here" line is her indirectly pointing out that she found Sakiko again, but conveying this to Tomori through a star metaphor (because, well, immediately before this line is when Sakiko springs in her mind). From there Uika picking up Tomori's lyrics and reading them is likely to foreshadow that Uika herself writes lyrics: as pointed out by the director in an interview, the two of them approach writing lyrics very differently. Her commenting that singing helps get your feelings across I interpret is coming more from her own heart than it was advice for Tomori directly (she doesn't know Tomori at all, so how would she know how to console her?), but what works, works.

I think the most malicious I could read this scene might be that Uika only talked to Tomori because she's an acquaintance of Sakiko's, but even then she seemed very supportive of Tomori reaching out to whoever she meant to with her writing (and Uika knows about Crychic falling out), so I doubt there was hidden ill intent. That said I don't really believe there's a "wrong" way to interpret the Ave Mujica cast as we know them now (other than like, thinking Sakiko only does the things she does to torment people and/or she's apathetic to Tomori or whatever). So feel free to keep reading the scene how your gut tells you to.