Storage and distribution works the same as for fossil methane (pressurized in cave systems/old gas wells).

Production is simple, and we yes, the efficiency is around 20-30% round-trip. But that's enough to handle up to ~30% of electricity supply with less than 2x overcapacity.

And that's assuming you don't just slap carbon capture on a gas turbine you feed with fractionally distilled oxygen (>99% should be easily enough) and enough exhaust back-feed to not melt the turbine blades. A diesel would probably deal better with the combustion temperatures, though.

And Fischer–Tropsch can turn captured carbon into piston-engine-suitable liquid fuel, if you'd need to.

IIRC, for Poland, we're talking about needing to build 10GW worth of solar generation to get 1GW into grid on average, or 4GW of wind. Assuming ~24GWh of storage to make it capable of providing that 1GW continuously.