Gigaton scale carbon capture using algae
newatlas.com
newatlas.com
I'd suggest looking for algae that grow in very alkaline water, in soda lakes. There are some in Africa, for example. Very alkaline water can contain much larger amounts of carbon, and one might be able to directly extract CO2 from air by spraying that alkaline solution upward to make fine droplets for large surface area air contact.
Your second point is interesting. I wonder about some complex with solar and concrete production, where high co2 outputs can be drawn through the water. I don’t know anything about water’s ability to dissolve co2, so apologies if that sounds ignorant.
Why can alkaline water absorb co2?
Lower pH goes in the other direction, hence the childhood classic experiment of vinegar and baking soda.