Why and how did papa start the fire?

Yes, Papa started the fire on purpose to serve as a distraction, so TJ could be taken safely to jail to face the charges for his crime. Papa thought the loss of his crop preferrable to the lynching of a young man. He wasn't trying to save his life, but he didn't want him murdered either. Had Mr. Logan challenged the men with his gun, he likely would have been hung alongside TJ. In setting the fire, he saved TJ and diffused the situation by forcing everyone to work together to stop the spread of the fire.

I don't think papa did it to serve a distration.