Is the milk spoiled when a thin layered textured appears in the bottom of pan?
This layer just means some milk proteins have cooked onto the bottom of the pan, and says nothing at all about the age or condition of the milk. It's more likely when you boil a smaller quantity due to the more rapid heating. During can help avoid this. 

However repeated heating and cooling isn't generally a good idea. With milk you can get away with it but it would be a better idea to boil only what you need (which would also be quicker and use less energy).