Is it right for a girl to refuse marriage if the groom insists that she should participate in an engagement and Mehndi (Asian singing and dancing ceremony) ceremonies, considering these are un-Islamic events?

All praise be to Allah and may His blessings and peace be on His last messenger, Muhammad,

Absolutely not. In fact, the girl should establish the covenant of marriage with one whose piety is his greatest asset. Because it is the piety, good manners and compatibility of the husband that will make her marriage a success.

Allah knows best.