Re: kids eating all day...
We went through this with all our kids when they were little. The oldest two could handle it a lot better as they got older, but the littlest two are too difficult to get to eat only at meal and snack times. The littlest is almost exclusively breastfed, but he sometimes wants to get in on snacking too.
Before my husband and I separated I used to have a stock of containers just for snacks. I don't know what happened, but at the end of his first deployment they seemed to grow legs. I used to fill each container with snacks and leave them in the fridge or pantry/cabinet at the end of every night. There was also a stock of granola bars, but I learned quickly that yogurt isn't an option with my kids because they'll eat nothing but that. With two dairy allergies in the house, we just can't do that anyway. They had their own shelf in the fridge and pantry/cabinet where all their snacks were kept. They were given freedom to take any of the snacks, as long as I didn't find them all over the house. At the end of the day I'd make more.
This worked great for us because I could also determine how many snacks to offer. If there were leftover snacks at the end of the day, I didn't make as many the next day. My goal was always to have all the snacks gone by the end of the day. If they started complaining they were hungry when the snacks were gone, I'd make up more batches for the next day. The kids really loved it when I made trail mix because they could trade out their favorite parts or share trail mix with different things in them each time so they all got variety.
If my boyfriend gets this job then we're going to look into buying some containers and going back to that. I think the older kids will have a little more freedom of choice when it comes to things like apples and oranges because they'll actually finish them when they take them, but the little ones need something a little more sized to how much they'll actually eat and I want to leave out limited amounts of things they'll try but may not like so much.
Bonus to doing it this way? I stopped having to dole out snacks all day! Instead I just had to open containers or granola bar packages every now and then. My kids loved the independence of being able to do it themselves so much that I never got asked or nagged about anything, which really worked for us.
Also, my oldest is pretty thin and the boys are average for their height (though my middle son is tall and heavy for his age), so I'm not too worried about how much they eat. Obviously they need the food. And they're very active and would prefer to work on art projects and watch movies than boredom eat, so that's also how I'm able to be pretty confident they're eating what they need.