
Well,
During the war he got badly injured and everyone belived he was dead. Actually he recovered and instead of claiming the throne he decided to keep the "Prince" dead so he could stay with Iris. By that point it was already decided that Iris' brother will marry the Princess (so he became King consort) and that Iris will permanently inherit the fief. Dean got married with Iris and helped her out to manage the territory in the shadows.

The First Prince took controle of the governement and put them in jail. Yuri was discovered to be a spy for a foreign kingdom wanting to invade them, but the second Prince refused to believe it. He escaped his cell and tried to save her, giving his life to protect her. Yuri was sentenced to death at the end of the story and was regretfull of what she did to the second prince because he proved that he actually meant it when he said that he loved her until death. She never tought that enyone would love her so truely. At the end Iris made her realize that she was in love with him too and that it wasn't just an act. As for the bad queen, I don't remember but it was probably a bad ending for her too, her son being dead and Dean wanting to take revenge on her for murdering his mother.

woah... I pity them.. it might be karma for them. Where did you get the source?
Well, i'm gonna be patiently wait for the next update. Oh! and also @Mokona44 did the 2nd prince realized his wrong actions? and also those minions of yuri based from the first chapter... well I expect that they should, becuz they really make our fl being inferior in her abilities, even though she shouldn't be..
hehe thanks for the spoilers

The second Prince never got to regret his actions nor understand what was trully happening. He likely tought that everything was a plot to overthrow him. To be fair both Iris and Dean were his political enemies so it is no wonder he would have a hard time trusting them. However since he was shown to be completely unfit as a ruler the coup d'état could't be helped. If he had been more aware of the outside world and stopped to listen to everyone equally, Iris's brother was even warning him but to no avail, he might have had a chance. For the others, the son of the previous Pope joigned Iris for a while to be able to stay in the noble society but he betrayed her again, leading to his execution. The knight who holded her down at the beginning started to realize that he was wrong to blindly follow the second Prince a little after the Pope incident. He didn't commit a sin and might become a man worthy to be called a knight if he keep is new mindset.

That depend on the version you want to read. It is completed in japanese, but the english version is at the last volume.
https://ncode.syosetu.com/n1337cn/
https://www.novelupdates.com/series/common-sense-of-a-dukes-daughter/
Why do I kinda want the third princess to rule??