Rune & Samantha Albright
I imagine that all that Rune knew about Samantha at first was that she plays as Ravenclaw's keeper. A fact that never really interested Rune, what with him scoffing at any sort of competitiveness between the Hogwarts houses, and that he doesn't actually care that much about the sport. He'll admit that she's good, better at it than he himself is, but, watching her geek out about the game from afar, inevitably he dismissed her as just another jock.
Until, they had a brief encounter in the library. Exchanging, borrowing, studying the same books regarding magics associated with animagi. From then on, his curiosity - or maybe suspicions is more accurate a description - has been peaked. He doesn't track her every movement, just more-or-less keeps an eye out, when avoiding his prefect duties. And when in his own form as a cat.
I'm hoping that eventually each unregistered animagus at Hogwarts will form a secret club/gang, but for now Rune's going to continue being his aloof self.
Rune & Minerva Fumihiko
If Mary requires a tutor in transfiguration, charms or DADA then Rune might be able to help? He might get a little exasperated by her kluziness, but he'd more-or-less stick it out.
Rune & Basil Snape
They can brood together in the Room of Requirement over cigarettes and firewhiskey, it'll be great.
Truthfully though, Linus is as grouchy as Rune is ... maybe a little bit nicer towards others, but he's not likely to annoy Rune. Rune's uncle, who had been raising him since his parents' deaths, is a charismatic if bigoted voice within the magical community at the moment, speaking against "halfbreeds" and the "discrimination against magical values and traditions." And I imagine that from his uncle Rune had heard a lot about Linus's father, knows what the man had stood for. Rune isn't the type to outright say as much to Linus though.
Maybe it'll be an offhanded comment, in the aftermath of another fist-fight. "Like father like son," or something like that. A misconception might be that Rune, like many Slytherins, would disagree and scoff at the view that Linus's father had upheld. Yet, with a little conversation, Linus could find that Rune actually thinks quite similarly to his late father. That he's very much against restrictions placed upon magic.