I have had birds lay a couple of eggs in one day over the years. I didn't actually see them lay but when I counted the number of birds and there was an extra egg so I assumed someone had to have layed the extra egg which meant one of the birds had to have layed two eggs that day. I believe the...
The most birds I've had is around 400. Now I'm down to around 200. I know how collecting eggs for my 400 was. I do have several coops all with access to the nest boxes outside the coops. I can't imagine climbing mountains to collect eggs.
I have some White Leghorns, my first, they have just started laying. They have a covered pen but if there is way for a couple of them to get out they will find it even though they have a big pen. I call them Houdini1 and Houdini2.
Don't worry. They will start laying when they are good and ready. I have had some of my Heritage breed that didn't start laying until they were around 36 weeks but most start laying by around 24 weeks. Some will start sooner and some will start later.