rationalize the authenticity of fluid mosaic model?

Answer 1

I think membrane sorting and signal transduction can be better explained keeping this model in mind. Moreover the fluidity can be explained by adding and removing cholesterol.

Answer 2

It's a good model because the phospholipid bilayer part explains why only lipid soluble molecules get through and the protein molecules and channels show how larger molecules get through at a slower rate.

Active transport concerns the movement of substances from a low to high concentration, against the concentration gradients, requiring energy. When they model how fast it occurs it correlates with how many available protein molecules are available in the cell membrane, ie, if they are all busy, active transport can only reach a certain maximum rate.

It also explains facilitated diffusion.

Hope this helps you as a starting point for further research.