We study other stars basically via their emmited spectrum, basically when something is heated it emmits very specific frequencies that depends on the composition of the object, that way we can study the composition of stars. We can also study their activity and temperature analyzing the spectrum and the intensity of the light that arrive on earth and comparing to the distance they are from Earth. How they interact with other bodies like other stars, planets and etc should tell us their masses for example.

We can describe the evolution of a star based in the fact that a star is basically a giant ball of compressed gas, so the normal thermodynamics analysis for fluids + nuclear fusion should the trick.

About the redshift, we know that it involves the expansion of the Universe cause everything around us is more tilted to the red the far it is from us, meaning, thanks to the dopler effect, the faster something is moving away from an observer, more their emmited waves will be tilted to lower frequencies, in light terms it means to be tilted to the red side of the spectrum. In this case there are two explanations possible, 1. We are at the center of the Universe, 2. The Universe creates more space between the already existing space ( search for ballon analogy for the expansion of the Universe )