Kill what is on the animal. Rest of article says they put them on preventative drugs after getting them cleaned up. So assume a very small life on dog.
Well, Dawn, vinegar and water in a spray bottle is what I use to clean the bathtub. I don't think the Dawn by itself would kill fleas, but maybe the vinegar would get through their crusty exteriors? Just guessing.
Any shampoo left on the dog for 5 minutes or longer will kill the fleas. The cause of death is suffocation. Dawn dish soap is a pretty common soap used for dog bathing. I've used it before to get rid of extreme filth on dogs. Vinegar is an excellent conditioner for hair of any type, dog or human, if you can get past smelling like a pickle.
I personally prefer to use an anti-itch shampoo so I can both kill the fleas and soothe the skin at the same time. Just me though.
As for repelling - no, it won't work as a repellent. Look for ingredients such as cloves, peppermint, etc. to repel.
Wash the dog in any shampoo - let set - dry dog throughly - sprinkle butt, ears, belly with DE (only works when dry - reapply anytime the dog gets wet)