Clarification on Inflation and Color Index

I have two questions:

1) We know that the Universe is expanding at an accelerating rate. And the proof for that is the graph where on the x axis we have redshift values and on the y axis we have magnitudes. From the data of observations we plot type Ia supernovae, now we can tell what Hubble's constants were at different times and so the conclusion is that the Universe is expanding at accelerating rate. I read that dark energy is said to explain the inflation, but where and how can i see that in the graph that i described? Maybe there is another graph that clearly shows the inflation caused by the dark energy? So this first question is about the relation of inflation and dark energy and what graph indicates that.
2) What is the physical importance of color index? My thoughts were that the calculation of color index consists of subtraction of magnitudes in different wavelengths, it cancels out the distance property to the star and therefore we can tell the temperature of the star without knowing the distance to it. Apparently, I was told that's not it, I wonder what is the real importance of this index.

Any explanations are appreciated, thank you!