If gas was $.10 / gallon, everything we consume would be cheaper because every single thing we buy is transported in trucks. A huge portion of what you pay for at the supermarket is the raw cost of getting a good to the shelf from the farm/factory.
If gas was $.10/gallon, cars would be cheaper. We wouldn't need ridiculously complex gas engines tuned to yield another 1 mpg, or electric cars with $30,000 of Lithium-ion. They could be low-mpg and cheap and it wouldn't matter.
If gas was $.10/gallon, everyone's wages would, effectively, increase since every person who owns a car would spend less on gas, which for many people is a lot of money.
If jet fuel was $.10/gallon, flying would be cheaper. Importing and exporting goods from faraway places would be cheaper.
Oh, lots of ways cheap gas would help me afford a flat! First of all it takes a ton of energy to build a home, so housing would be fundamentally cheaper. Then, every month, I'd be spending less money on heating or air conditioning. I'd also be spending less of my own money on transportation (either through less gas costs, or buses/trains being cheaper). Then since goods are cheaper at the store, I have more money to spend at the store.
There is one mode of transportation that is currently REALLY cheap and that's huge ships. That's why we import so much from China -- sending a huge ship across the ocean is really cheap. If all forms of transit were that cheap (trucks, flights) the world would be very different.
If shipping is cheap why does goods go from Chine to US not from US to China?
Would cheap energy lower land costs for a house or flat? Cheap energy would improve situation. But a lot of competition comes from productivity and wages. Low wages in Asia made possible to import goods cheaper from Asia rather than produce locally.
Cheap energy is good, but i worry more about our ability to afford those things.