Can a person love a girl and can talk with her before marriage, and if parents are not agree on marriage and what should the couple do? Please explain this.

It really depends on your culture, your beliefs.

Where I live, Canada, and with my beliefs, talking to the opposite sex is no big deal, and as a mom with two teenagers, I want them to date whoever they like, and when it comes time to marry, who they marry is their choice, not mine. If they have sex before marriage, I'm okay with that too. Once they're adults they get to make their own decisions.

It doesn't sound like that's the culture you live in. Maybe telling us more about the rules your parents have, and the culture you live in, and the beliefs you have, would help us answer your question better.

In a society where parents must pick and/or agree to a marriage,
It is not correct to have physical contact. Talking may or may not be allowed, depending on culture.

If one already breaks those rules, then they do not believe in the rules or respect the culture for them. At that point, they may decide to marry anyway, against family wishes.
But then suffer the results.

I think your best bet here my friend is to talk to your parents about your feelings, wishes, and intentions for this girl, and let THEM explain their rules, and expectations for both your conduct and behavior in this matter.

In this way you will have clarity from your parents before you even bring this to the girl you love. That may help you get facts before you cause a conflict with them, or at least help you make a decision about how you should proceed.