good questions..... My gal layed an egg on 20 weeks to the day. Each chicken is different, but all my girls are around 20 weeks and most are squatting, maybe 4 that aren't. My first hen squatted and a week later, her first egg!
We used to look all around the yard too looking for eggs (you sound a lot like me), because we were expecting it'd be any day. We have the golf balls in the nest box and that's where she laid. Egg eating.... we came home from church on sunday and went outside (very hot) and saw some yolk on the grass, and found the whites a few inches away. At the floor of the coop we found another shell less egg (monday). Sunday night a hen laid a shell less egg right behind us!
I heard that when chickens lay soft or shell less eggs, then it's anyone's game. If they are eating the eggs, it's normal. It's when they eat the hard shelled that there's a time to worry. Evidence of egg eating, look around, and look at their beaks for yolk.