
I don't understand where this is going, why did she kiss her?

Because she loves her. This entire chapter is entirely about her inner thought process coming to the conclusion that she loves Sumika. Next chap will probably give further clarity, but I suspect she's started to realize that her idea of romance was naive.
Loving someone deeply is wanting to make them happy. It's when their happiness makes you happy. The strongest relationships are the partnerships where both participants are motivated by a desire to enrich each *others* lives.

I need someone to help me because my memory is lacking. So Haegu killed Mian's father, but then she was kidnapped??? And that's when Haegu decided to keep her??

When Haegu killed Mian's father, Haegu didn't know that Mian saw that, Haegu was shocked and didn't know what to do, she left her there for the cleaners team (Who covers up the crime) to deal with her but the cleaners didn't take Mian with them so she ended up being taken by child traffickers, who abused her and drugged her. Once Haegu found out that Mian is in the hand of child traffickers, she went to save her and took her with her to raise her and especially to raise Mian to take revenge on her.
Is this the new Yuri curse? Not adapting even the ln now??