1. Chickens in general you shouldn't be afraid to touch, the nest boxes where they lay eggs also is totally fine to mess with (such as taking eggs, cleaning it, etc) However BROODY hens CAN be mean and just be cautious, most do peck or bite but if you've been bit by a cat or a dog it's not bad (although can be surprising)
2. You can try to move a broody hen to a different nest, although I'm not sure of the success rates for this. Some people do it fine, others hen's don't take. Ours would always go back to their original nest.
3. Yes you can add fertile eggs under a broody hen, leaving unfertilized eggs under a broody hen can lead to rotten eggs however so it's best to keep an eye on what your hen is laying on (some people mark eggs, however we collect daily so it's not an issue for our not-too-big-flock)
4. A chicken lays an egg just about every day. I think technically their bodies create an egg every 36 hours? Some people believe some hens can lay two eggs in one day, I personally have never seen this however, and can't imagine if it is possible that it would be good for their bodies anyway.
5. You can't make a hen lay eggs. Once a pullet is mature, she'll typically lay eggs (100-200 a year I believe) for a few years before slowing down in production. We have a 5 year old hen still laying an egg a day during all seasons besides winter.
6. You don't have to do anything special to make your rooster mate with your hens, besides of course having a rooster, and hens. It's highly variable on the rooster himself and the ladies but if you intend on getting a rooster make sure he has enough ladies so that he doesn't overbreed the hens, stress them out, and injure them.
7. Hand raising chicks generally results in fairly tame bird, treats, daily interaction, going at a slow pace generally works well (not rushing, harassing or frightening the birds, remember they're technically prey animals)
8. How big is the coop? How long are they being shut in? Do they have a run, and how large is it? Why do you want to shut them in? Do the roosters get along, and how many hens are there?
9. 
https://www.backyardchickens.com/articles/how-to-get-a-chicken-to-lay-in-the-nestbox.66573/ Here's a good article on showing ladies where to lay