Yes, it's most likely not only from guilt but from his own selfish reasons as well because like I said, he's spoiled and naive. The prince is still super young, but I understand what you mean. He's a very easily hateful character because of the way he handles things which can also be seen as manipulative. He's narrow-minded and always tries to get what he wants. However, part of the reason why he's overprotective and manipulative, without knowing because it doesn't seem like anyone really scolds him for anything, is due to guilt of bringing her here.
He simply doesn't care about the female lead because she wasn't pretty. Once again, very narrow-minded. His character in itself is purposely made so that he's unreasonable and hateful but all of this can still be fixed. We obviously can't really judge him too much yet because I just think he's still a kid and has lots to learn. He's petty and does very childish things but that doesn't make him an antagonist that we want to beat up or anything. He just needs to learn how to be mature. I honestly don't know how the King could not control the child though, he's such a respectful and polite man.
That's the thing, that's apart of her personality. Being surrounded by so many people it becomes hard to not rely on them. She's still somewhat of a child, considering she was only in high school. After being thrown into an unknown world, believing you're all by yourself, and not knowing how the world worked, of course she would rely on the person who first stretched out his hands to her. It's not her fault that she became so timid either. The prince himself is to blame for shielding her from everything and anything. She somewhat knows that the prince is being too overprotective, like the chapter where she said she wanted to get stronger and go to the West Forest instead, but after being manipulated and protected by him for so long, she's lost her own will and continues to rely on him.
I honestly really like Aria's character because it shows how she is being warped by the Prince but still showing signs that she feels this is wrong. She simply needs a push to tell her what is right and what is wrong, to find her own voice, and I think this can be accomplished by meeting the female lead or somehow finding a way to talk to the prince's fiancee. To me, she's very pitiful and I wish her the best. She may be annoying now because of how weak she seems but she still has some hope to break out of his control, make new friends, become independent, and learn about the world herself. What's really holding her back is how the Prince is making her feel like she's not from this world, that she can't get along with anyone and that everything is foreign to her. All she needs is to get away from that and learn that she does have a place in this new world and that it's okay to live here, just like the female lead has learned.

I think wthe second prince should be the crown prince and the first prince shouldn't be the king after all he's an idiot
And that bitch should stop talking to engaged men wtf what if she's alone so what that doesn't give her the right to take those men from thier fiancée (╯°Д °)╯╧╧