What follows is a little graphic. But, if you want to flush things like paper towels down the toilet, leave it in there overnight. By morning the wood fibers with be softened, and it will probably flush down easily. (Also, and this is the graphic part. If you're a man, you can always just pee on it. That often softens the wood fibers right away. But not always.) But if you flush and the toilet overflows, never flush again. Toilets are designed that they never overflow if you flush them once and it doesn't go down. If you flus again (or flush three times like an aunt of mine once did) it will definitely get all over the floor.
It depends on the type of toilet paper. Good stuff is softened sufficiently, the second it hits the water. I recall stuff in a box in the 60s or 70s, which was like tracing paper. It came in a box folded similarly to how tissues are packed.
Yes flushing paper towels down the john,make sure its watered down and as small as you can get it so it passes easily........