What kind of flow rate would be necessary to pull CO2 out of the ocean faster than it dissolves from the air, and is that achievable without affecting the surroundings?

CO2 wouldn’t be pulled out of the ocean. You’d have to liquify it from air in a different process. The molecular pumps are used to extract dissolved ions or solutes from sea water and only act as fast as diffusion.

So this is desalination? That seems unrelated.

I listed cleaning up toxic waste and co2 sequestration as separate things, yes.