I guess that is possible. I usually put thin cardboard and paper in the paper shredder, it's much faster but I will be sure to do a tear check before shredding them.

Plastic hides out in a lot of places. There's plastic mesh in almost all teabags, unfortunately, if you're adding any of those. If you're adding other kinds of food scraps, consider whether hidden packaging may be sneaking into your compost collection.

Yes there are lots of things that will not decompose. Windows from envelopes/junk mail and those crazy PLU stickers from fruit will live longer than most of us.

You may live near a saw mill, a wood-working or cabinet shop, or another business which produces clean sawdust as a waste. Many people use tree leaves. When shredded (passing over them with a lawn mower for instance,) they are excellent sources of quickly-deteriorating 'browns'. Wood chips from tree trimmers work well. They are often more bulky than just a small tumbler will need, but on the other hand, if you have a small section of a yard where you can keep a pile, they decompose quickly on their own also, and make a good mulch material.

The little brown cardboard boxes that mushrooms come in are now coated with plastic. Remember the old wax coated cups? They are now paper fiber sandwiched between layers of plastic film. Arghh.

BTW, the balls are not unusual in a tumbler. If you searched this forum for 'tumbler balls' you would find numerous mentions of them. They are not a problem as long as your tumbler doesn't smell bad, which would mean it's probably too wet. They form naturally from the tumbling when the material is the right size and stickiness to stick together.