Some questions from my English class

1.Are these sentences the same?

-Not both of my brothers are teachers.

-Both of my brothers are not teachers.

-Neither of my brothers are teachers.

2.Do these sentences make sense?

-We had the class' the fan running.

-We had the class the fan running.

-We had the class light on.

3.Which of these sentences are correct?

-I think it's very important to study hard.

-I think it very important to study hard.

-I think it our duty to study hard.

-I think it's our duty to study hard.

Thanks.