Although I mostly agree with the analysis, I think you misunderstood a couple of things:
Time to write an essay about Toudou as a character to explain how we got here.
So Toudou has a few main traits that are constantly reinforced throughout the series. One, she is extremely selfish with her need for attention. Two, she is kind and forgiving to those around her and that are kind back. Three, she is very stubborn, only accepting how she sees fit for right and wrong and other peoples character.
I agree with you on those points. She is selfish, wants to be the center of attention, wants to be praised. Simply put, she wants people to WANT TO BE LIKE HER. This of course is a consequence of how she grew up and the home life she's been leading up to this point. Parents that for one reason or another neglected her, and only saw her as a problem child when all she wanted was a bit of the love and attention they were granting her sister. She wants to be envied by everyone around her the way she envies her sister.
Her kindness is shown just throughout the series without much need for examples, as she will go out of her way for her friends. Such as trying to convince Banryuu (Yakuza) to come to school as a favor to Yomotosuke (Prez) or all the work put in for the band. While her forgiveness has some slight complications. Kamisada (Yankee) and Rin (Kouhai) she forgave due to actually getting to know them and figuring them out as people. Saya was much the same in this chapter, as she realizes she was only doing bad things out of necessity than malice. The revenge against her teacher, while somewhat over the top, was clear she didn't actually mean to cause harm. She just wanted to make him slip and laugh at him.
I don't believe she EVER wanted to convince Banryuu to come back to school though. All the opposite really. The prez used TD's character as a way to get Banryuu to come back to school, but TD herself was always against it. The game of Cops and Robbers was never about Banryuu going back to school, it was all about TD not becoming a slave to Banryuu.
She didn't really so much as forgive Rin, as more like she was under the assumption that Rin was under the influence of the drug at the time, and she thought she had already gotten her revenge. Her realization that Rin was actually trying to motivate her is what gave her the courage to fight during the last stretch of dodgeball competition. If you notice, she never really held Rin responsible, she just held a bit of animosity towards her, but that all went away when they were open with each other about their feelings (no forgiveness necessary).
The stubbornness is based on how set in her ways she is. With her belief that she's not into yuri (TITLE DROP), unwilling to accept anyone else's views on someone that go against how she views them with Yanagi (Delinquent), not accepting that ghosts can be real, etc. She'll usually only relent on things if she is set to gain a benefit from it.
Her problem was not the fact Yanagi was being blamed of the petty theft, her problem was that nobody did anything to understand WHY she would do that. Knowing how honest Yanagi is, it didn't make logical sense for her to steal like that, and the fact nobody questioned her, rather, they just judged her after the fact is what pissed her off. She doesn't believe Yanagi is a saint, that is not what she was arguing about. She was angry nobody was there for her and she was just cast off by her group of "friends."
Which leads into the selfishness. A large portion of this can be explained in story due to trauma from being neglected by her parents over Arare (Little Sister). The entire premise with getting her teacher to drink a love potion is formed from this selfish need for attention. She expresses that she doesn't actually care about the teacher and more just wanted him to dote and favor her. She was more after the social status that preferential treatment would bring than an actual relationship. I feel this one doesn't need much more explanation than that, as nearly all escalations in the series or convincing that is used on Toudou in the series is through her getting more attention.
Yes, that is correct.
Her constant belief that no one could be into her (dismissing Rin or Kamisada's teasing as malice, not thinking Yanagi actually likes her with any of her affection, and not understanding that Kurohime wants to be with her) might also be a small inferiority complex. Her never wanting to try at sports due to believing she's only a disappointment and thinking she's an inadequete partner that no one would want. Though this point is more an inferring from small implications.
She is also terrified of getting hurt. Rin traumatized her with her training (all those messed up fingers lol). That's the main reason why she doesn't really go for any sport clubs. Even Rin pointed that out the very first time they met in this story (chapter 7). This also explains her uncanny Iruma-like ability to dodge any kind of danger that comes her way. As for being dense towards the affection of others? It depends on the person and the way they approach her. She had no real issues with accepting Rin's and later Yanagi's affection, even if they were not in a real relationship, she is willing AND interested in doing lewd things with girls she likes.
Also no idea why she's being so affectionate with Toki (president crew tall one with hair bun). Thinking back, others have rarely ever gone out of there way to help Toudou, so she could be generally affectionate when thankful. Though the date is more just her being oblivious, I recall her doing the same with Rin after Cops & Robbers and not thinking anything of it than just grabbing a bite to eat.
You got this one wrong. Rin was the one that called it "going to out to dinner." TD called it a date, to which Rin quickly corrected her. In fact, and this was right at the end of the Cops & Robbers game, TD told Rin that even if they lost, she had no issue with going out on dates with her, just as long as she invited her (once again, she feels uncomfortable taking that first step at this point, and is relying on another person to "pick her").
Mainly writing all this to just say. Toudou has not changed much as a person. She's still oblivious to hers and everyone else's feelings, still acts in self interest, and still helps her friends. Not to mention, as sad as it might be, her relationship with Rin is somewhat built on a lie of rushed feelings due to Arare's schemings. I can only hope they don't crash and burn, as Rin and her are adorable. No idea where we'll go from here but I fully welcome Toki and Saya to the harem. Maybe even Oikawa, though, I think they're going for more of a partners in crime dynamic with her.
I'd say she has changed, as she is A LOT MORE confident in stepping forward and facing anyone that dares get in the way of her current goal. She is not oblivious, she just knows that the girls all have different levels of "normal," so she acts accordingly to whoever is her current companion.
As for Rin and TD's relationship being built on a lie. I don't know where you got this from. Sure, a series of misunderstanding led Rin to eventually confess her feelings for TD (who at the time thought Rin was under the influence of the love drug). But the moment she realized Rin was never drugged, and those were her real feelings, TD took them to heart and actually mulled over how to respond to said feelings. The chocolates did not influence her decision, those only made her super horny. If you notice, during the phone conversation, TD comes clean, and is very clear about what she feels. She didn't want to rush things with Rin, because she is afraid she'd lose what they had built up to this point. She asked her if it was okay to take things slow, little by little falling in love with each other. And Rin agreed to it. That is when they officially became lovers. Also, the chocolates only made TD yearn for the person she held dearly in her heart, so it makes sense that she would've been thinking of Rin since she was the only person who had confess to her without the use of the love potion.