question

When Yash wasn't happy that Rahul didn't want to marry Naina why didn't Rahul just confront him? Yash was questioning Rahul's choice of Anjali by saying "Can this girl understand our traditions?", "Can she understand our ethics and principles?", "Can she adhere to the values of this family?", "How could you think this girl could be a part of my family?", why didn't Rahul just talk back and say "Yes Papa, she can be a part of this family, just because she is of a lower caste doesn't mean she doesn't know the normal traditions and values of an indian family." Instead of saying "I will do what you say" and then going back on his promise and marrying Anjali, he could've just talked back to Yash about Anjali's good character and could've said that she is just as good as Naina. He could've also said "would you prefer it if i married someone whom I didn't love and remain unhappy or would you prefer it if i married someone whom I love and be happy for the rest of my life?"
I believe it was just that he wasn't on equal footing with his father. He did try to bring this matter to his father but the father just made him feel very badly.

I think Rahul did a stupid thing by marrying Anjali because he was going behind Yash's back. He didn't even marry her straight after the funeral. He may have married her a few days after the funeral so was he just keeping quiet about his planned marriage to Anjali? The fact that he went behind his back could've been another reason why Yash disowned him. If he was just honest and said "Anjali lost her father, how can you expect me to leave her now?" Yash might've understood and given permission to him to marry Anjali.
Rahul had to go behind his father's back because Yash totally disapproved of this marriage. On the other hand, Rahul so Anjali's pain and his heart just went out to her. He simply couldn't help himself.

By the way I felt sorry for Anjali and Rahul because they didn't have a proper indian wedding. Anjali should be wearing a nice saree or a grand lehenga and Rahul should be wearing a nice sherwani. Anjali was just wearing a normal salwar and Rahul was in his casual clothes.
True, but this was a rushed wedding. Also, remember at the end that Yash honored Anjali by welcoming her to the family before his other son's wedding.

By the way how did Rohan know who Pooja was in the college? Did he follow her from her house to college?
Yes he did. He specifically went to that school.

Also I never got this- how did Yash finally realise his mistake after 10 years? Was it because his mother died or because there was too much distance between him and Nandini ever since Rahul got kicked out?
All of the above. Remember that he didn't even know he was a grandfather just because he was being stubborn. He turned into a bad husband by keeping her son away from her. He lost his stature in front of his wife. He finally realized that Anjali just wanted to honor him as the elder.

Also when Rahul and Anjali go back to India do they stay there? Coz Rahul had his full time job in London, what happened to that? Or did he work for his dad?
It's a given that Anjali and Rahul come back to India and that Rahul takes over the running of the business (with his brother's help, of course). They would most likely live in a wing of that mansion.