I feed mine egg shells too, sometimes they eat them, sometimes they don't. I have a small pan of the oystershell on the side, they mostly ignore it, but if they were needing it, they would.
You are going to get some soft shell eggs, or some misshapen eggs, especially at first. These are living creatures, not machines, and it takes a bit to get the kinks worked out. People often freak about the soft-shell eggs and want to do something! And you can, but truthfully it will works its way out if you do nothing.
In the summer, I wash my water's in cider vinegar - to reduce algae. Do not put it in their water all the time. I once contacted a professional breeder about what he fed, and he said, any good commercial feed, is best. They have to meet standards, and are tested and have been scientifically researched to meet the needs of chickens.
Try and keep a flock, and enjoy the birds you have now, KNOWING that the birds will change with time. Give them the best life you can, but do not feel guilty when you loose one. Generally speaking, chickens are not real long lived, and some have genetic miscues, that you can do nothing about. Some people on here, have very old chickens, but it is very unrealistic to expect all of yours to live for a long time. It is better to plan on loosing a few, and adding a few each year. I keep a flock, and have for years, but the birds come in and go out of the flock.
When do they lay, pretty much you are fairly confident that you have the only non-laying flock in the country, and you have been sure they should be laying, and have given up hope. You find the treasure.
Good luck, this is a fun hobby