Could be - the limiting factor after CO2 access is sunlight. Microalgae have the tendency to self-shade which limits growth. Again, photosynthesis is also a very complex process and there are many pathways to increasing efficiency. Lots of work is being done on improving photon activation in microalgae, meaning fewer photons are required to trigger individual photosynthesis reactions.

> Do plants pull it out of the water directly?

yes

> I've also wondered about whatever mineralization happens in making sea shells - I understand that's another natural process that fixes CO2, is that something that could be replicated, artificially or through growing a high concentration of little shellfish?

Again possible however I believe shells are limited by the availability of calcium ions, finding an appropriate organism etc. I am sure it is possible to genetically engineer some kind of ultra fast growth oyster hybrid. The question is can it be done in reasonable time, cost of deployment etc etc