"His grandmother used to sing."
Translation:उसकी नानी गाती थीं।
Both थीं and थी make for a valid translation. The plural verb "गाती थीं" used with the singular noun phrase "उसकी नानी" acts as an honorific plural and is only mandatory when the speaker doesn't want to come off as disrespectful towards the person being referred to.
True. थी should also be allowed.
Moreover उसकी नानी/दादी गाया करती थीं should also be added.
Indeed. Looks like that usage has been avoided altogether in this course as a translation for "used to".
It's implied that, because it is his/her grandmother, there is a plural of respect which is why it's the plural थीं instead of singular थी.
It is used in some cases to denote respect but yea both should be accepted.