
I don't blame the mother for not trying, both her and the father knew that she wasnt good. Villain Pryde is an awful, despicable person, even though she had unconditional love from her father (he tried in the game and she still stayed evil). As a Queen who has the ability of foresight, she knew that Villain Pryde was luckily never meant to be the heir for her kingdom. She prioritized whoever will lead her kingdom with stern love and kindness, and it wasn't Villain Pryde.
Please remember that Villain Pryde would've never changed if it wasn't her PREVIOUS LIFE'S memories.

Her father was that person to step up and try. Though it's not ideal, one parent is usually enough to love a child. But even so, Villain Pryde still grew up to be an entitled narcissist. In my opinion, I have no faith in Villain Pryde to be a good person even if she had outside guidance from both her parents. I fully believe her destiny has changed because she became an entirely different person.

Excuse me the whole basis of her becoming a villain was that it was obvious her mother was preferential to her sister and never even saw her once and then her father died. The only parent and person who was there for her, in this version she stopped her father from dying, but in the game the villain had become devastated from losing her last pillar and that's why she became that way.

I'm not shaming anyone for thinking so, but I just don't think anyone else should take responsibility for the terrible things she does.
It's not like she was a good person because her father loved her. It's not like her father was her only hope and after he was gone Then she spiralled into becoming a villain. That's not the case: that's not the bases of her becoming a villain. Even when he was alive, she did self-indulgent things, like psychologically fucking up her servants by threatening them with punishments and death penalties. She believed that she was entitled to everything and demanded everything to be hers, that she should be the best and she should only be given the best. Anyone who had a lower status were not just lower than her but less than her, and she took joy in reminding them that difference in power. In her world, only she was important and everyone else was mobs for her to play with.
Me, personally, I have a single parent taking care of me. No matter how devastated I am when they die, I am not going to psychologically fuck with my step brother with false promises of going to see his mom if he enslaves himself, nor am I going to tell him to go and kill his mother. Villain Pryde should take responsibility for her terrible, egoistic actions. I don't believe in blaming her dead father nor her mother for the terrible things she's done nor the terrible things she was going to do.
I believe both nurture and nature exist. And some people are just born terrible.

I understand we got attached to her when she was a child, so to a lot of us, she reminds us of when she was a baby. But we need to stop babying her and recognize that she's grown and was CANONICALLY RECOGNIZED as the MASTER of the house. Aka she was acknowledged as someone who was capable of representing the DUKE and managing the affairs of a DUCHY. She is fully capable of deciding who she likes for HERSELF.
Even so, we watched her grow up and we know what type of environment she lived in. She was FAR from being groomed, she developed a normal and healthy affection for him and it's perfectly normal for girls to feel attraction to guys older than them.
We need to STOP acting like it's shameful for women to have age gap relationships when they're perfectly capable of deciding things for themselves. We need to STOP looking down on women who, when they were young, had a (non-blood related) friend that they considered their brother, but when they grew up, realized that friend meant more to them than just a brother.
YOU'RE IN YOUR RIGHTS TO FEEL UNCOMFORTABLE, but you are also in your rights to STOP reading things that make you uncomfortable.

How old was she before she reincarnated? How old is her character "Princess Yerenica"? How old is the main lead? I cant find their ages. I read somewhere that they had an age gap but i assumed that they were consenting people capable of making decisions for themselves. They're relationship hasn't even progressed that much anyway so I didn't understand why people were disapproving of it.

Nymph Project is the same thing as this. Idk y they have different names.
http://www.mangago.zone/read-manga/nymph_project/

I can't remember the reason, why does she want to hide her identity from general?

She's hiding it because she is embarrassed. When he first saw her walking in the city and asked her if she was the one who helped him, she accidentally replied that it wasn't her. So now she doesn't want him to find out and think she's a liar. Really just a slippery slope and very naive of her, but it's true to her character of being a teenage girl.
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Poor Sana (ToT) he doesnt know he's hated