I don't think the king registers his feelings on a romantic (or related) level (I think it's very much on a this is my rabbit, my pet, level) so I don't think the intent is creepy, but his actions sure are 🤢
As for the grand duke, his emotions might evolve, but right now I don't think he's really in love with her. It's just that as the first person to have scolded him who also wouldn't allow him to ignore her despite the difference in social power, she's left a more lasting impression than anyone else he's ever met.
I still hope she'll earn her freedom somewhere down the line and meet someone outside the palace (or not, this story has enough interesting elements that it could potentially do without romance)