Hey luvs....what you are doing is making paper!
You are transforming the denim threads from woven fibers to unwoven fibers and molding them into 100% cotton paper objects.
Yes, you can put anything into the wet fibers to embelish them.
You might try other bits of fabric scrap to make other colors, but remember you will only get a solid color. Printed patterns will be lost as the fibers separate from each other in the blender. They might go paper bag brown or muddy
The reason stretch denim doesn't work is because it has stretchy rubber or plastic fibers in it.
The shapes you put in the cookie cutters will dry faster if they are thinner. You don't want to fill the molds up.
..also, press out as much water as you can. Put a paper towel on them, press them with a pan bottom, peel the paper towel off. You can add stuff anytime.
After they are dry you can do anything to them you can do to paper!
( You might be surprised to find out that Y'all have just joined the prestigeous and ancient society of 100% rag papermakers who have been doing this for hundreds of years! - google it and see!)
Yes, you can use paper from your shredder! There are how to-s online, but it is the same technique basically.