Stupid question, if we find a commercially viable way of converting CO2 into fuel is there a danger of "global cooling" because people will get too greedy with this?
No: the atmospheric CO2 is at the bottom of the energy hill. In order to turn it in to fuel you need to pump in all the energy originally extracted from the fuel, then some more.
After you've re-expended the entire 20th century's worth of fossil fuels energy equivalent in sucking CO2 out of the atmosphere, not burned it, and stored it in a country-sized propane tank, then maybe we're back to 19th-century temperatures.
"Bottom of the energy hill" is a chemist's short hand way of saying that we can't practically extract energy from CO2 reacting with anything useful, meaning chemically this is at the bottom end of reactions that happen without energy input. To convert it into something reactive, you need to invest energy to split it up again into its constituent parts, which is what happens during photosynthesis.
"Bottom of the energy hill" is a useful term in a lab. However the earth is not a chemistry lab. We cannot ignore photosynthesis outside of a lab as it is a factor that exists.
Even if it winds up back in the atmosphere, it's displaced an equivalent amount of new CO2 going into the atmosphere.
Pulling enough CO2 to make a kilogram of propane and then burning that kilogram of propane for electricity is still better than burning a kilogram of freshly fracked propane.
One offsets consumption. One just adds consumption.
Only if your source of electric doesn't add CO2. If you burn coal to make propane you are worse off CO2 wise than using regular propane. We have a lot of wind and solar, but most places they are still a minor part of the electric mix (if this applies to you, it wouldn't be hard to get a lot more wind/solar in your grid).
The application of this is not in energy production or - realistically - CO2 capture on a global scale. This takes huge amounts of energy to do and requires a sophisticated chemical synthesis in the background in order to replenish the catalyst.
Pretty much the only reason to do this would be because you're specifically interested in generating propane. For example, it could be very useful for ISRU on other planets, or to generate propane "for free" from a solar setup.
If your goal is energy production, you'd just use the output of solar panels directly without this costly step in the middle. If you want to store energy locally, electrolyzing water into H and O would be hugely more cost effective. But propane is a more dense fuel that would be useful for mobile applications such as ships and cars, and can also be used as a raw material in chemical synthesis.
Theoretically it would be possible, but we would just release some carbon from other sources, there's a lot of it in various rocks if fossil fuels somehow expired (we still have a lot of those).
Taking the carbon from the atmosphere will always be more expensive than from some carbon-rich rocks that form a huge fraction of the Earth's crust.
In fact, our most effective ways to take carbon out of the atmosphere today all involve a step of letting some mineral turn into one of this carbon-rich ones, and extracting it from there.
It'll always be more expensive to extract carbon from the atmosphere, but if it produces a valuable byproduct and the power to run the process is very cheap (excess solar) it might still pencil out.
When you have surplus photovoltaic capacity — an increasingly common situation — you could turn it to electrolysis. You still have to pay for the equipment, but it sounds like it could be pretty cheap.
It would cut out the cost of mining, and possibly a lot of transportation costs, if you can use the products nearby.
Yes, and before humans the earth was on a cooling trend, though only measurable on a geological time scale (millions of years). A little plant matter gets converted to charcoal and then coal every years. Though biology mostly trys to get at that carbon first.
After you've re-expended the entire 20th century's worth of fossil fuels energy equivalent in sucking CO2 out of the atmosphere, not burned it, and stored it in a country-sized propane tank, then maybe we're back to 19th-century temperatures.