Some key insights from the article:
Basically, what they did was to look at how much batteries would be needed in a given area to provide constant power supply at least 97% of the time, and the calculate the costs of that solar+battery setup compared to coal and nuclear.
No, none of that has much to do with CO2 output besides transportation.
Nuclear power needs a lot of concrete. Concrete releases a lot of CO2 during production. It does eventually reabsorb it as it cures over a decade or two. IIRC, it might even be CO2 net negative eventually.