(experiment 1: diffusion through a liquid) does the rate of diffusion correcspond with the molecular weight of the dye?

The answer to this question would be: False

The rate of diffusion should not be influenced by molecular weight. Big molecule might not be able to pass the membrane though.
Diffusion happens when there is a difference/gradient in the concentration of the molecules. If the difference is higher, then the diffusion rate will be increased.

Well, both latitude and intensity of light affect temperature because, the higher the light intensity, the higher the temperature and since latitude is the measure of how close you are to the equator, then the closer to the equator you are, the higher the temperature is.