Ours free range, so in the spring, summer, and fall months, they eat a lot of grass, weeds, and Kale from the garden.
Mine generally ignore veggies in favor of fruit, but one thing I read that I have found is true, at least with mine:
We are in the desert and the ground is just empty dirt so there's nothing for them to forage. In addition to their feed pellets we give them fresh or frozen fruits and vegetables nearly every day: spinach, kale, broccoli, wheat grass, corn, peas, blueberries, cantaloupe, etc. Keeping chickens in the desert is expensive!
Wheat grass is the only thing I've been able to grow reliably and that is in containers. We don't have any topsoil so we have to buy all the soil for a garden, that is also expensive but I would definitely like to grow more! I've tried moringas twice but they wouldn't take. I'm going to try again next year because we'd really like them for the chickens and ourselves.
One thing to maybe plan for is to create some of your own soil, with the assistance of your ever-helpful chicken poopers. Soil (in terms of gardening) is a combination of inorganic materials from your underlying rock profile plus organic material from plants and animals, including dead leaves, grass clippings, food scraps and, yes, chicken poop
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That really depends though - corn can be classified in different ways depending on who you ask or how you use it. Botanically speaking, it's actually a fruit. Culinarily, it's a vegetable if you eat the kernels while they are still soft (like sweet corn on the cob or in a can). It's considered a grain only when it's fully mature and dry, the kind you feed to livestock. So if corn scraps from what the humans ate were fed to the chickens, then yes that counts as vegetables, and can make the chickens fat since corn is high in carbs.
As I explained above, corn is considered a vegetable in the way people eat it, so if it came from human food scraps, then it's a vegetable and can make chickens fat since it's high in carbs. Chickens are drawn to the sweetness and may not be able to regulate themselves. Other vegetables that are high in sugar/carbs and can make chickens fat include root vegetables (beets, carrots, sweet potato etc.), legumes (peas, beans, lentils), squashes etc. "Vegetables" is a large category that extends far beyond the leafy green low-calorie things we may first associate with the word, and a lot of them can overload the chickens' diet with unnecessary calories if fed frequently or in large amounts.
That's why I don't like that rule, and am not even sure it's a "rule", rather just something being tossed around, potentially borrowed from other animal species care (like pet fish - feed as much as they can clean up in X minutes, because there's no other good way to dose their food). The experienced keepers recommend the more precise guideline of 10% for treats for chickens, and that's a lot more realistic. The 15-20 minute rule is way too vague and depends on too many things - what kind of treats, how are they being delivered, how many chickens are eating them, how fast are the chickens eating, etc. - a WIDE margin of error, and a wide variance in the calories potentially consumed. High calorie treats like scratch grains can be inhaled in large amounts within seconds, vs. plucking at greens stuffed in a treats cage can take a lot longer for far fewer total calories consumed.
