Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.

Yes, it is permissible to wish to marry someone from any race or culture. Allah said:

“O you people we have created you from a male and a female and we have made you nations and tribes so you may know one another. Indeed the best of you are those of piety.” (Al-Hujurat 49:13)

And one of the ways to get to know one another is marriage.

As for the second question, for a female’s first marriage, she must have the approval of her father or wali.

Marriage is not a relationship between two people only, but rather between two families. The family of the bride represented by her father must welcome you as their son in law.

Islam gave the right for the girl to veto anyone imposed on her by parents and gave the parents the veto to reject any one imposed on them by the girl.

Best marriages are those that are welcomed by all family members on both sides. The Prophet (peace be upon him) said: “any women marrying without consent of her Wali, then her marriage is not valid.” (Ahmad)

So, a female cannot marry without her father’s approval.

Now having said that, the parents are advised to look for faith, manners and good character in a groom when making a decision for their daughters not that of wealth or race or color.