yes but the whole cycle of making an egg takes 28 days, so they are constantly starting the cycle every day, which makes them egg laying machines as you put it. ;D
Yes you are right, if you give chickens antibiotics you can't eat their eggs for at least 28 days after the antibiotics are finished, cause it takes 28 days for an egg to form inside the chickens body.
Our birds quite like a wee drop of layers mash which is the same as pellets but in powder form, as long as you don't get it wet as it goes sour quick when wet. ;D