This may be a stupid question.

I don't believe that a rooster has any effect on egg productions. Also The hen will lay eggs for days then start to sit on them. They don't start developing until she sits on them so they all hatch around the same time.

 

Nope. The egg laying is independent of the rooster. The frequency has to do with the amount of daylight. I believe one per day is the most they do. Mine are laying one every three days right now, although that should improve as the days get longer.

When they lay to hatch, the eggs don't start developing until the hen starts incubating them. They just sit in stasis sort of. They'll all hatch on or about the same day.

Welcome to BYC!

 

They may actually lay less with a rooster. He chases them around all the time, and it is quite tiring to fend off a rooster, so then tay don't have what it takes to lay.
A broody hen waits to sit until she has a "clutch" of eggs and then will sit on them pretty much non stop. So the eggs all hatch about 21 days after she stays on the nest. She will get off once or twice a day to poop and eat and drink.

My mother always said: there are no stupid questions, only stupid answers. If you had to ask it, then it is a valid question.

 

A rooster does not increase egg laying, all he does is fertilize the eggs.