Assuming that energy units roughly equate to dollars, it would be immensely cheaper to cut our emissions today, as much as possible, than to keep emitting CO2 at our current rates and then hope to capture it back in the future. The reasons we behave in this illogical fashion:
1. The costs of acting now and the costs of acting in the future are going to be bared by different entities. Thus some entities can profit out of this, to the detriment of the rest of us.
2. The nominal economic cost will be higher, but it might become economically more viable, still, just plainly out of desperation when things get really bad.
So to answer you question, maybe yes. Not entirely though. CO2 can be captured back, maybe, but the damage to human societies and the environment cannot be fixed. But nonetheless, this should not be an excuse to delay action on climate change!
Reversed as in CO2 levels brought back to preindustrial levels within a few lifetimes, not known.
The "warming" is a small part of the overall problem; CO2 increases are impacting a far wider range of conditions, including those in your own body, and that of your food. The temperature changes just capture the imagination better.
Other than stopping burning so darn much, our two go-to strategies are "artificial weathering" where we unearth carbonaceous rock and convert CO2 into bicarbonate, pulling it out of the cycle, and "ocean fertilization", where we unleash the power of aquaculture by dumping mineral nutrients into large swaths of ocean, whereby a new crop of plant critters will absorb the CO2 and add it to the food chain.
Most other ideas either make the problem worse (blocking out part of the sun, for instance), or fail to move the needle.
My upcoming book Fat Gas (first few chapters at fatgas.com) is a useful resource on the subject.
Unmelting all the ice that melted in that time would cost a lot more.
You can absolutely take CO2 out of the air and produce useful output. It's physically possible, no problem. It's not at all profitable, though. Not much reason to produce synthetic gasoline at $20 a gallon when you can make it from fossil petroleum for $3 a gallon.
This is why global warming mitigation efforts have focused on reducing emissions instead of carbon capture.