Welcome to the forum!
Your best bet is to read, read, and read some more. Here's a good book to start with:
http://www.storey.com/book_detail.php?isbn=9781603424691&cat=Animals & Farming
You can also browse in the forum here for a wealth of information on pretty much every topic having to do with the chickens. This is a wonderful place for that.
I'll try to take a crack at the specific questions you've already posed. Different breeds of chickens have different laying abilities. If you pick a breed known for being good egg layers, you could expect to average 2 eggs a day from 3, perhaps 4, hens. Remember, though, they're not machines, and egg laying tends to taper off and even stop during the winter, during broodiness, and as the hen ages. Many of the breeds that pump out a lot of eggs in the first year or two of their lives taper off dramatically after that. Here's a quick guide to different breeds:
https://www.backyardchickens.com/breeds/breed-chart
Yes, many breeds of chickens can easily fly over a 6 foot fence unless you clip their wing feathers (which will also take away much of their ability to escape from predators while free ranging though).
You can keep chickens inside a secure, outdoor run. A rule of thumb often quoted here is 10 square feet per bird of outdoor space plus 4 square feet per bird of indoor space, although more room is always better. Again, much depends on the breed of chicken you choose; some tolerate confinement better than others. And your climate is also a factor. In very cold winter climates where chickens will often be confined inside during the winter months, building more than 4 square foot of indoor space per bird would be wise.
Dirt with wood chips is doable, but in my opinion sand is better. You can sift the droppings easily out of the sand with a kitty litter or sand scoop. Whatever you use in your run, just make sure the area drains well and doesn't retain moisture. Accumulated chicken droppings plus wet conditions mean stink. Artificial grass? I wouldn't think so. The chickens would probably eat it, and I can't imagine that would be good for them. Not to mention a host of other problems like it would get nasty very quickly.
I've read about people leaving chickens unattended for periods as long as 4 or 5 days, but it's not ideal. The eggs build up in the nests, making it more likely that one wil lend up broken, then teaching the chickens that there's tasty stuff to eat inside an egg, which could lead them to become egg eaters (a bad thing, if you want to eat the eggs yourself). Then there's the problem of some mishap to the water supply leaving the flock without water for that long a period. You can do it, but just be aware of the risks involved. It's really better to design your coop setup to make it easy for someone to come by once a day, collect the eggs, and make sure all is well.
