Because the pronoun "мій" is masculine while "сім'я" is feminine.

It is singular and not plural for the same reason it is in English and every other language that I know.

I was wondering the same thing.

Well, because it is kind of a collective noun. My family is big - family is singular as well.

Бо це здебільшого взаємозамінні слова. Є відтіночок: сім'я - це найрідніші, а родина - це рід, більш широке коло родичів.

Моя сім'я = my family. Мої батьки = my parents. Family is a bit more than just parents :)