Is there repentance for one who lied, wronged, caused the severing of kinship ties, and broke off an engagement, and are his acts of worship accepted despite his feeling of Allah's wrath upon him?

You must apologize to the person you wronged and explain the reason for your mistake; otherwise, you may expose yourself to Allah's punishment. If your repentance is sincere and fulfills its conditions, then it is accepted and validates your acts of worship.