Is the continuation of a girl's phone communication with a young man who wishes to marry her, but is rejected by her family, considered a sin that prevents her prayers from being answered?

You must stop conversing with the foreign young man and obey your parents in their refusal. You may try to convince them again if that is effective and does not lead to corruption. It is advised to fear Allah and seek another husband who possesses good character and religious commitment if approval is not granted, while also increasing supplications.