Starting sentences with 'and'

English

There were a terrible accident yesterday.

He bought her flowers she sent the flowers back.

He made her a birthday present. He bought her chocolate.

Which of these sentences is an incomplete sentence?

He went to the cinema. and he went to the gym.

He went to the cinema. And he went to the gym.

He went to the cinema. And He went to the gym.

He went to the cinema. He went to the gym.