In order to improve the mileage, we would suggest you drive slower. Driving fast can reduce your fuel efficiency by up to 33% if you are travelling above 60 mph. It is best to change gears appropriately and match the gear and the RPM carefully.
The main reason your spare tire is smaller is that they are meant to take up less space in your vehicle. The spares usually have a smaller diameter, narrower width, and shallower tread, which means they make great space-savers. This is especially important to maximize the storage area in your boot.