1) You MIGHT have enough airflow. It depends on how big the holes are. Keep the lid on loose. The lid is not to keep the worms in, but to keep the light out. Did you drill holes on the bottom? It is hard to manage moisture in a plastic bin if there are no drainage holes.

2) The moisture level sounds about right. Shredded paper tends to clump. I prefer to mix it with another bedding type. I use about 50% cardboard. But paper will work by itself.

3) My guess is that you have overfed. If the food decomposes too quickly, you could have a smelly mess on your hands, especially if you don't have drainage in your bin. If the food decomposes more slowly, the worms should be able to keep up. If the bin starts to smell, the worms should take care of the smell in a day or two. Some foods smell for a couple of days no matter what you do, like onions, or cabbage or broccoli.

4) By all means, get your kids involved. This will be a great learning experience for them.

The problem with lack of drainage is that food tends to have more moisture than the bin really needs. As you feed the bin, the moisture increases until you have water pooling on the bottom of the bin. This water will cause the bottom of the bin to go anaerobic. You really want drainage holes on the bottom of the bin, and some sort of catch basin to catch whatever drains out. I have my bin sitting inside of another Rubbermaid tub. The lower Rubbermaid tub has six 2-liter soda bottles cut down to 4 inches high sitting upside down in the tub. This holds the worm bin up so that the two bins don't get stuck together, and there is some airflow into the lower bin.

Thanks sbryce. I drilled holes in the top, bottom and all the sides and have the tub sitting up on some old 2x4's with a tray underneath to catch whatever liquid is produced. All of the holes are 1/8". Is that big enough?
I'll make sure to not add anymore waste until the worms have made it through what's already in there.

You might be OK if you leave the lid loose, but I would want more air circulation than that. I would put a line of holes as close to the top rim as I could. That way you can have air circulation without letting in much light.

If you don't feed again until the food that is in the bin is mostly gone, you should be in good shape. If the food in the bin is in fairly big chunks, it should break down slowly, and your worms will be able to keep up.