It makes the burning of fossil fuels more efficient, e.g. you can X tons of coal to produce Y MW of power and get Z additional gallons of gas. But it's really a stretch to call this carbon neutral.
There are other processes that produce CO2. E.g., cement manufacture.
Yes, because Prometheus fuels is trying to extract from atmosphere. Scavenging industrial CO2 byproduct is something you can only do opportunistically.
There are plenty of opportunities. Those will be taken up first.