Question

on their birthday还是on their birthdays

Answer 1

如果是在同一天就用on their birthday；如果不在同一天就用on their birthdays。

Answer 2

二个都对：第一个是twins，第二个不是一家人

Answer 3

on their birthdays
在他们的生日

双语例句
1
We can also send them gifts on their birthdays.
我们也可以在他们的生日时寄送礼物。

2
They celebrate them on their birthdays or name days.
他们会在孩子们生日或命名日的时候为他们庆祝。