"Mother lives at home."
Translation:माँ घर में रहती हैं।
No. It has to be रहती हैं since रहती can be used for both singular and plural feminine words. But it is true that हैं has to be used to indicate that it is plural (or in this case singular but polite). रहते would be used if you for example said father instead of mother, as it only applies for masculine words.