"I don't think Haibara and Conan fit together at all, because the way they think is too different"
I don't know where you get that from. it is evident that you do not follow the plot. if ai pinna from a different way to Conan is because Conan is impulsive, Ai makes him see the reality of the situation, which is dangerous.
Ran doesn't know anything to begin with.
her ways of thinking are opposite, Ran and Shinichi are totally opposite worlds, Ran does not fit into the plot, she is there by script and the author disguises it as coherent. While Shinichiusa his speeches to convince the People, Ran is short fuse, and uses his strength to chastise and threaten.
Currently, Ai collaborates with Conan, in the last case Ai smiled for solving the case with Shinichi and helping the entity. it is obvious that they are becoming one.