Premium gas is usually cleaner, regardless of whether it increases MPG. The funk that gets in your motor causes degraded performance over time. Generally, you will get more life out of spark plugs, fuel filter, and anything gas touches in the motor. Some cars are rated premium only, don't fool with it if that is what the manufacturer says - they're not lying.
New cars that specify premium only will misfire or run in a degraded mode until you switch gas and have it reset at the dealer, at that point they will void your waranty. I'm aware of someone who had a car like mine and torched the motor doing this... This is especially true if your motor has a turbo/super charger.
Synthetic oils are of a much higher and durable grade, and cleaner. They also last longer, your oil changes can be 1/year 10,000+ miles. (You do have to make sure you are getting an oil filter that pairs with this extended mileage.) Certain engines, especially performance ones have higher tolerances and will fail under normal oil - you cannot use it, unless you want to lose the vehicle warranty/trash the vehicle. Some of the performance oils last 15,000 miles, so compared to changing your oil every 3-5k it's also more convenient. If the manufacturer recommends synthetic only you are just playing with fire.