How many are eaten at a time depends on how many big the snake is and how many snakes there are. Many 6 foot-plus rat snakes have found my hen's nest boxes through the years, and snakes that size eat 4 large eggs per day, every single day. I go to extreme lengths to protect broodies with chicks in extremely secure pens, yet nearly every year a snake manages to defeat my attempts and gains entrance and eats chicks. Just this year a rat snake gained entrance and ate 2 of 10 one-week-old chicks. We had flooding rains from the time those chicks were born, and just enough dirt washed out underneath the pen to allow the snake to slither underneath. (It was a 4-foot rat snake.) I never saw the snake at the time, but after I reinforced the ground barriers, the snake came back for another meal a week later. This time it didn't gain entrance, and I killed the snake. Can't be certain it was the same snake, but for reasons I won't list here, I'm nearly certain it was.)
In your photo, a snake could easily crawl up those table legs and into the brooder. Or at least "my" snakes definitely could. I'm sorry you and your broody are losing are losing eggs and chicks. IF an egg still exists and you want to keep your hen in your current brooder, I would Securely attach 1/2" hardware cloth over the top of the brooder, making sure there is no place a snake can wiggle in. And I do mean Securely. I once had a juvenile copperhead (still had yellow tail-tip) get under a pen where the opening was so small that the snake actually got snagged on 1/2" hardware cloth as it entered underneath. It bit/killed one chick, but could neither eat the chick nor escape because it was snagged. It was very angry at its predicament, and struck at me several times (while still snagged) before I killed it.
