Yes it's completed! Basically they get back together. Princess is super annoying bc she tries so hard to get ML to marry her! She gets embarrassed everytime. Grandfather also takes FL side since he also loves her like family. Turns out the doctor was helping the prince cover up the murders he was doing. Prince was the one who killed the FL's sister too. Prince then take FL to piss of ML. Doctor dies helping her get her. Prince gets caught and Princess decides that taken the throne is better so she helps with arresting the prince.
I can share the novel if you like
Here you go ヾ(❀╹◡╹)ノ~
https://rainofsnow.com/seeking-for-your-forgiveness/#chapter
Spoiler…
From those last chapters from season 1, I immediately got the idea that the Prince killed her sister… I mean, she was sneaky about a man probably high class ? The Prince was known to be a womanizer and He was nowhere to be found at the same period she was killed and all police officers where on a search for him ? How convenient. I guess the MC didn’t even think about it because it must sound absurd to her but all the pieces seem too suspicious to not be explored.

I recommend reading the novel instead