Sports? I was always under the impression that Haibara actually liked Soccer/Football, which is the sport that we are referring to, more than Ran. Haibara seems to think that one player on Osaka(excuse me if I'm wrong, it's been a while and frankly I'm a lazy bum to look it up) shares a somewhat similar fate to her. Because of this she starts to get into soccer and become a fan of that team. Ran might possess like common knowledge of the sport due to just idle chatter and from the news, but I don't believe she shares the same passion as Ai does.
The similar set of ideals is a valid point, but then again, most behaving citizens also believe in justice and determination. I'll admit that at first Ai was an ice queen, and didn't share the same sense of justice as Conan did, but she's changed a lot in this 600 episode series. She acts a lot like Conan's partner-in-crime (or rather, justice) in the later half of the series.
She sometimes trusts him... there have been so many moments where Ran starts to catch on and thinks Shinichi is lying to her. The whole debacle around episode 100ish when Yukiko picks up Conan, and how Ran was seriously on the verge of unmasking Conan's identity, only to be saved by his mother. The whole cell phone deal too, around the 400ish episodes, where she tried to guess Shinichi's passcode. Ran has her suspicions, no doubt.
Why do you say no? There are many times during the series, that Conan and Ai share similar and hilarious facial expressions, meaning they have the same reactions to things.
Conan of course, is a mystery/deduction otaku. While Ran..for the most part respects Shinichi's hobby, she sometimes get ticked off on how much he loves Holmes/mysteries/etc. Ai, on the otherhand, finds it fascinating. When the two first met, I believe she said something along the lines of "your style of deduction/ love of mysteries is interesting" with her face only mere centimeters away from Conan's (episode 130-140ish, when the Detective Boys were at that house).