Do you think large cells and small cells carry out diffusion and osmosis at equal efficiency? why or why not?

The answer to this question would be: No, the bigger cell will have a higher rate of osmosis/diffusion.

Osmosis and diffusion will happen in all of the surfaces of the cell membrane. The Bigger cell will have bigger volume and wider membrane surface area. That means the cell can do diffusion and osmosis in the wider area, thus have more speed than smaller cells.