I don't believe so, but Giardia can be transmitted to people, and of course most forms of worms too like round, hook, and tape. Not too pleasent to think about, but if you're concerned you can always get checked out.
Yes they can. Coccidia is encased in a tough egg-like shell. It hatches once it's ingested. Through hand washing and keeping puppy bowls away from human food preparation areas is important. Bleach does not kill it as some have said in other posts. Extreme heat will kill it on hard surfaces.
I've read and been told by vets that coccidia is species-specific and humans can't contract the organism from dogs. I downloaded a good article about it from the Lambriar Vet Supply website, but they don't have the article there any more. If anyone would like it I can attach it to a direct email.
