I'll post something random. Kitamura only talked to Ryuuji for his own reputation. The "guy who talks to the scariest guy in the school" can become pretty popular, esp with his personality. Of course, now that he is popular himself, he has no need to be 'close' to Ryuuji, which is when he started telling everyone that Ryuuji is not scary. Of course, he's not going to outright ignore him as he does have that image to protect.
I don't know about the yakuza thing(though that wooden sword in ep 1 would make you think that), but Taiga could have had problems expressing herself, particularly her parents, and esp since she's small. Getting further and further frustrated from being ignored, but no knowledge in how to relieve it, she reaches her limit, resulting in an physical outburst full of all her anxiety and repressed frustration, causing everyone around her to notice. From then on, she comes to the conclusion that in order for others to listen to what she has to say, she has to be loud and get physical, as that is the way she acknowledges that others acknowledge what she is saying or doing. She wants to live in a new place, so that she can start over with her newfound theology on socialism. However, this is the 'self' that was the result of her circumstances, not her true 'self'. Minorin was the only person that really wanted to listen to her, so Taiga can be her true 'self' with her. As for Taiga with Ryuuji... I'm still trying to garner a guess on that one >,<.
Ryuuji doesn't just see Taiga as some klutzy, loud, strong-willed, semi-helpless girl. What Ryuuji really sees in Taiga is, in perspective, himself. By helping Taiga, who is a mirror of himself, he will become the person he strives to be... uh... brimming w/self-confidence and stuff >.>(lazy w/the wording there). In essence, to have the ability to help Taiga is to also have the ability to help himself(redundant?), so he will continue to help fulfill her goal to get with Kitamura(though of course, it's also because he's just a great guy
).
Yes this is all[random and fun] speculation, no, I don't read and haven't read the novels, and yes I've read the manga, but all of this is purely based on what is in the anime.