Mine was to work tax policy to incentivize companies to make all their packaging shiny and white, incentivize people to litter, and disincentivize everybody from recycling.
My friend's was to use a giant rocket to push the earth farther away from the sun
Yes... plus some electronics, like a rectifier, an inverter and control circuitry.
Yes... that's partly what is was conceived to do. It also can compensate for the irregularities in demand.
For storage of solar and wind power, this is a complex matter, and the short answer is "it depends". For demand management, it makes sense now.
It is desirable to use hydro plants (where they exist) as swing producers. Pumped storage is not quite as energy-efficient as battery storage (roughly 75% for pumped vs 85% for Li batteries), though it can be cost-effective, in places where large, elevated reservoirs already exist.
But all this is besides the point, which is: There are proposals to "solve" global warming, which are implementable now, with today's technology, which furthermore have side effects which are on balance positive (like clean air in the cities).