So first, Yuri is an immortal mage/magician/whatever. He fell in love with a guy hundreds of years ago and once his love died, Yuri tried all sorts of black/death/curse/whatever magic in order to die as well so he could be with his lover. However, nothing worked, he became immortal, and now his current body is slowly dying/rotting. But in present times, his past lover reincarnated as the current King, so now Yuri went and bespelled/enchanted/magic-seduced the king and most of the other surrounding men to love solely him. It's kind of why the novel has a slight BL tone because Yuri basically made his whatever love-spell so powerful in order to fully entrap the King to him that it's now affecting all the other men as well. Women and maids not included in this mess.
Second, the poor nameless baby is in fact Yuri's child. Yuri convinced the King to let him sleep with the Queen in order for them to have his child to raise as a loving couple. Essentially, the Queen was not okay with this, Yuri then raped her with his black magic, and she begrudgingly carried the baby to term on the King's orders. This is also the reason why Yuri had the head maid killed because she saw that Yuri using his black magic to conceive the child and wanted to shut her up. However, the REAL reason why Yuri did this, is because as I previously stated, his body is currently dying but he wants to stay with his King lover for as long as possible and what better way to do that then to create a baby from both his magic and genetics to use as his new vessel? Ugh. . . .
Third - as for our maid MC - later on once the Queen possibly dies from sickness and she becomes able to go back home to her original world. Because the MC doesn't really see the need for her to be there anymore with the Queen now dead and Yuri+King being all lovey-dovey and far from receiving any sort of punishment, she decides she has no more interest in remaining in the novel world. However, by this time, she has already seduced a couple of men herself. Her blonde teacher for one and the red-haired guard for two, the one that's always with her. Not sure if there are other men or who they are. Thus when she leaves, I read, that it's the red-haired guard that decides to go with her back to her world.