What if the mayor left the camp then joined again?

I think no

Yes they can become the mayor again if it is within 30 days and no one else has claimed it during that time. Someone else can only claim it after the mayor has been absent and they would have to hold "acting mayor" position for 30 days. Anytime during the duration of anyone's "acting mayor" status, if the mayor were to log in, the mayor would automatically go back to him/her.