1- Somehow people didn't understand it, but it's been heavily implied he isn't his father's son, but his biological mother's affair result, while she was married with his father. The other guy didn't want a kid so his dad just kicked her out and kept the kid.
It's either that or she found a new partner but he didn't want the kid to come together with her.
2- The mom is pushing them to get together because he's the one PERSON that she got along with like that outside of her family, so her happiness lays with him. Not only that, she knows her daughter and can see she likes him that way and is helping.
It's possibly also probably the main reason she didn't take his surname... yet.
Basically the only thing stopping them from being together is his own complications about having the blood of a cheater and believing he doesn't deserve happiness because he's probably just like his mother, that is, his fear of being like her.
The sad part in all this is that Hinata got absolutely robbed. She HAS been very slow while he is very dense. But she also barely got to high school, it's like she didn't get her chance.
This does have a lot of chapters, so I'll end up seeing how much I got wrong.