You shouldn't need to provide a light for them this time of year. There are definitely more than enough hours of daylight now.
Just be certain they have enough to drink and that they are getting enough to eat. If you are feeding them scratch, I'd take that away altogether as they don't need those extra calories because of the heat right now.
Everyone's chickens start slowing down when it gets hot, so don't worry yourself to much.
I just put a fan in my coop up high so no one can get hurt open the windows from some more airflow it cut the heat way down and egg production is back up in our coop. but now none of them want to go out to forage they stay in all day staying cool haha chicken AC
It could. If you decrease the length of light they get it can cause a molt even if they are still seeing over 12 hours of daylight. Any change can induce stress. Any stress can reduce egg laying and could start a molt. It is very likely the heat or some other explanation, but you might look for signs of molting as another possible explanation.