Orthodox Jews do not drive cars on the Sabbath because it involves lighting a fire. Starting a car is like creating a fire, which burns fuel and gives the car energy. Kindling fire is one of the 39 types of work that the Torah prohibits on the Sabbath.
The Hebrew word Sabbath (in various forms) means both "rest" and "seventh." Saturday, as the 7th day of the week, is the Sabbath Day, the day of rest, for Orthodox Jews. The rest can be answered best with the previous answer's link.