Both of those statements are false: synthetic fuels exist now. Last I checked you could buy synthetic fuel for about 2-3 times what regular fuel of the same types cost. Germany was doing synthetic fuels in WWII. South Africa did them when under embargo for their racist policies. Now they are mostly used by racers - where allowed they are enough better to make a win against regular fuel (assuming great drivers and well tuned cars).
Maybe, but all you really need is a source of CO for the process to work. Coal or natural gas are easy sources, but with some energy input we can make it from CO2, Photosynthesis is the most obvious way.
Sustainable really depends on how much we need. There is probably enough wind energy for the process, so long as we only use it for things where high energy density is needed. That means drive an EV car or electrified transit, but we can use synthetic fuel for airplanes. Maybe, this last is mostly my guess, it is a real problem to work on.
