The first thing I want to pay attention to is the engagement, it can be a game for the public, just like Rika's account. Rika could do it in order to hide that she was a whore, showing that she was a good and decent girl. Why did the engagement break happen, since it was a fake. By the way, Matsuo didn't mention anything about the engagement, although as he said, he and Rika were good friends.
The second nuance is that Rika turns to Misato for help. Why should Ricke ask for help from someone who holds a grudge against her? And why should Rika tell the details of the quarrel with Soska? There are two answers here, the first one is Rika is desperate, the second one is that Misato doesn't agree on something.
The third nuance is the photo that blackmailed Misato. How did you get it? Either the phone was hacked, or the photo was processed in the photo editor (Fotoshop).
The fourth nuance is the rumour about the "whore's house". How did he come about? And who spread it? As for me, there are two candidates: Misato and Iwabuchi. Misato did it out of resentment against Rika. Iwabuchi did it because Rika cheated him, robbed him or because of the breakup of the engagement.
For the "first" point, I won't argue with your theory because I find it interesting. So, it could be true or not.
As for the "second" point, after i re-reading and closely examining the previous chapters, I think there is still a chance that the person who called Misato and gave her the job to trap Sousuke was someone who disguised as Rika using her old number. Why do I think this?
1. Misato hasn't been in contact with Rika for a long time, so the chance Misato still remembering Rika's voice through the phone is too low, this could be a loophole for someone disguise as her.
2. As we know, Rika's secret account has been inactive for a long time. There is a possibility that it’s not that Rika didn't want to use it anymore, but that she couldn't access it because her old phone was taken by someone (in this case perhaps Iwabuchi), including her old number which is now being used by an imposter to contact Misato.
3. Misato said this was a strange job coming from Rika. Yes, it is very strange also for me, because ever since Misato found out Rika had a relationship with Iwabuchi and could use her naked photos to blackmail her, Rika never exploited her. Also this is seems contradicts for me with what Rika has done to Sousuke so far. All this time, i think Rika is more look like to trying to keep Sousuke with her, like she using the excuse that she is pregnant and trying to convince him that the baby is his. Although a lot people right now assumptions Rika is always trying to trap Sousuke, none of that is certain yet right ? So, in my opinion, for now, it's better not to assume that the person contacting Misato is the real Rika. And also in PTA trip if we examines more clearly mori testimony, rika doesn't clearly said to target Sousuke to take the SD with raw video. She only said she want to catch up someone who anonymously stalking their momonga account lately but shingo mori missunderstand that person as Sousuke and drag him instead.
For the "third" point, I’m sorry, I don't quite understand what you meant, but I will try to answer it. In chapter 69, Misato already opened up about her past. Iwabuchi has Misato's naked photos because of the work Misato was forced to do. She sent the photo to her first prostitution client (job from iwabuchi), but it seems that client forwarded the photo to Iwabuchi as well. Then, as we know, Rika and Iwabuchi have a relationship that time, and Rika didn't deny that she collaborated with Iwabuchi to trap Misato. So, based on this, the issue regarding Misato's photos shouldn't be confusing.
For the "fourth" point, yes, I also have thoughts closly similar to yours regarding the "whore house". That is why I have said in my previous comment that if Iwabuchi is the main villain, many questions in this story will be answered and make sense. Also if iwabuchi is main villain it will opens up more story possibilities that more make sense than Rika being the villain and solely reason because she is a psychopath, narcissist, has a fetish, and anymore.