Hmmm... I am not claiming that anything you said was wrong, but a few things stick out at me.

here was the first:

"Getting up a to a million tons of CO2 a year would require two kilometers of 20-meter high, 8-meter thick fans running 24/7/365 for 0.0025% of annual CO2 emissions, and 0.0001% of the historical problem"

okay, so thats a volume of 0.32 cubic Km. Multiply that by 1000 to capture 2.5% of the annual problem and we have 320 cubic kilometers. Divide that by the land area of the earth (40,000) and you have 8 cubic meters (a 2 meter on a side box) for every square kilometer on the earth. Depending on how you pose it, it doesnt seem all that crazy. The better analysis here would be around energy usage to create the box, vs the carbon capture abilities vs other means. a 2 meter box on every square kilometer on earth is an absurd amount of production. :)

The rest has a lot of valid analysis. Its absurd. However I don't think your analysis of the structure is valid.

"So far they’ve just built the framework for the facility. It clearly has the strength to support its own weight. But just looking at it makes it fairly clear that it’s not going to support over 700,000 tons more at the top."

The Burj Kalifa weighs in at 2.2 million tons and the bottom structure holds that. So structures can clearly hold immense weight. If you look at each "elevator shaft" the idea that four of 1/4 of each column could support that weight doesnt seem absurd to me. It all depends on the cross sections of the concrete and the grade of concrete. Said another way, can each vertical column hold 27 metric tons?

a 2ftx2ft column should do it, no?

https://ncma.org/resource/allowable-stress-design-of-concrete-masonry-columns/