Haha, I think some of these questions aren't meant to have answers just yet. I'm fairly sure we don't know a solid motive yet for for what Law was trying to do to Jesse in the Moritat. My best guess is that he was either trying to satisfy personal feeling of love and possession towards Jesse or he erased a memory that we don't know about yet because that is the purpose of the Moritat after all. I think that Jesse's mother was simply removing an obstacle when she had Law's parents killed because she had wanted Law to stay beside her son and in the company and they were throwing a wrench in her plans. As far as I understand, that is correct about Jesse not wanting Law to be a dog, hence when he mentioned that he was just granting Law's wish not to be controlled. If he had any ties to the Brown family I think he would have been controlled in a way so Jesse removed himself as well and went to an inferior college to free Law from himself. I'm sure we will soon find out what Law intends to do to Jesse, but from their interactions so far I don't think the ultimate goal is to harm him. The brown haired maid found out about Jesse's hemophilia and so Law originally used her as an experiment for the Moritat. No idea why she is now helping to administer it but she is likely just a pawn.
now I'm plenty convinced that people doesn't read some chapters xD sorry I didn't want sound rude at all but the reason was explained in a lot of chapters from the past. Law told a lot of his intentions on his memories from the past. His pv literally show us why he did everything.
Law did Moritat because he wanted to control Jesse's mind.
since Law was never a sane person,he had these type of insane feelings for Jesse probably cus Jesse is all that he can not be.
He wanted Jesse to feel everything what he felt (I mean fear,desperation, confusion, deep love for him,craziness) and that was just what Law made him feel inside of Moritat. He totally played with Jesse's mind because he thought that was the only way to make Jesse feel all these things because the real Jesse would never have this type of feelings in real life even if Law could have wanted to kill him in front of his own face.
Law was pretty frustated because Jesse is a person who has no fear at all(unlike him who since childhood has lived with all kinds of fears)
Law is angry with Jesse because he blames Jesse of his own craziness at some point too, he thinks Jesse is who causes that he has these type of "bad feelings" ,Law doesn't accept this is his own self who is not sane.
That's why you see Jesse saying to Law (a lot of times) that Law always use him as excuse to his problems and choices when he is the only one who make shit in his own.
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And the one who killed Law's parents is the mother of Jesse because she wanted to adopt Law who would be a big help to the Brown Company?
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we still don't know that but I think this will be revealed in the last chapter,Law still gonna explain more things to Jesse in the last chapter (they gonna have a talk here) and we will get know another info too.
I forgot
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And because Jesse didn't want Law to be a dog to his mother, he requested her mother to let go of Law and banish him somewhere?
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yes, Jesse just wanted to fullfil Law's wish(as colofurl said)Jesse did this because Law's wish was not to be controlled.
On some chapters, Law told to Jesse that he wants to equal with him and don't want to be controlled by him. This is also the reason why Jesse never did Law his own dog or trained him as his dog either. He could have done it but he respected and fullfil Law's wish cus he clearly had special feelings for Law too.
Oh yes, thank you for your explanation. ^^
And no. I did read all the chapters. It's just that some of their conversations don't make sense to me. And I wonder whether my understanding of the story is really the story the author wants to convey.
After reading the chapters, here is my understanding of the strory:
Law's parents wanted to use Law to be close to Jesse who is the heir of the great Brown Company. Law experienced a lot of emotional pain, fear, and rejection since childhood (due to his family situation, the people who were criticizing him for being close to Jesse, and Jesse whom he love but hate at the same time.)
And his only happiness was whenever Jesse paid attention to him and needed him. But that happiness was not enough for him anymore because he also wanted to know what Jesse was really feeling and thinking about him. He felt frustrated that Jesse was always calm (?) and it was as if he can control everything around him. That Jesse was so superior and he felt so inferior to Jesse. That Jesse didn't really care about him when in fact, he was so in love with Jesse. He also wanted Jesse to be at the same level as him- physically, emotionally and mentally.
And when he came to know about Moritat and Jesse's hemophilia, Law thought that it was his chance to control Jesse and make him mine.
Now, he didn't care about anything anymore (whether it was about his parents or other people). He would do anything just to satisfy what he's feeling for Jesse.
and as for Jesse, he really cared for Law but he was not that expressive. Maybe Jesse was like that due to his family circumstances (people look up to them- actually they;re worshipping them already).
And yeah, these are some of my undertsandng of the story. I just want to clarify whether the other people also understand the story the same way I do. or there are some details that I am wrong so I want others to share their thoughts too ^^

Can someone please clarify to me what is really happening there? I'm confused on some parts. =((
So from the flashbacks, why did Law want to do the Moritat? Why is it that he is frustrated with Jesse?
And the one who killed Law's parents is the mother of Jesse because she wanted to adopt Law who would be a big help to the Brown Company?
And because Jesse didn't want Law to be a dog to his mother, he requested her mother to let go of Law and banish him somewhere?
But then why is Jesse now in a pathetic position and what does law intend to do to Jesse?
what's the role of the brown haired maid?
PLEASE TELL ME PLEASEEEE >< THANK YOU~!