In regards to town and city charters did people vote for their mayor and city council? If not who appointed the people in charge, and when did citizens gain the right to vote someone into office?

Good question!

While there were cases where local government was appointed, more often with chartered towns and cities these positions were elected. The franchise tended to be restricted to either freeholders or people who had “the freedom of the city” (also known as “freemen”) which like the freehold was often associated with some sort of property requirement or payment.