I only prewash if I think the color may bleed. I test it before washing. I use starch/spray and iron the fabric before cutting. The steam and heat will shrink the fabric if it is going to shrink.
About batting, I never pre shrink batting. I wouldn't use it if I had to. Scrim is a good thing for cotton batting, keeps the batting from shredding. There are too many sites online that will inform you of everything you need to know about batting. Many think bamboo is the miracle fiber for batting, it's not. Many think the label of 100% cotton won't have scrim, it does.
I grow a few cotton plants in my yard to use for stuffing for small projects. It's as natural and as organic as you can get but it would make a horrible batting.