If you want a lot of milk and a small goat you might want to look at Nigerian Dwarfs instead of Pygmys. NDs are dairy goats, but small. Do you have to milk twice a day? Yes and no. If you keep the babies with the mom you can milk less, but then of coarse you will get less milk. Some does will milk longer than others on one freshening- but I've never heard of that being common with NDs. I've heard of some LaManchas and other full sized milk breeds that will be in milk for 2+years with one freshening, but it's highly dependent on genetics and the individual goat. If you skip several days milking your goat- especially if you don't have babies nursing- your goat can get mastitis, and infection, so you don't want to do that.
Yes, you want two. However, you could get one wether (castrated male) since they make great companions and pets, they eat less than a doe in milk too.
Food depends a lot on how much grass/browse they have, how thrifty the animal is, and if they are growing or in milk. We feed our full size wether 1/4 c feed a day and he's plenty chubby and it's our lean time for grass and weeds here. NDs are usually pretty easy keepers, but any animal giving lots of milk will eat a lot more feed.
You'll want separate feeding areas for the chickens (we feed our chickens 2xs a day while the goats are tied and eating) but the chicken coop is in the goat yard and they free range together. The goats love to sleep and play on top of our chicken coop. The get a long the same with our ducks too.
Your shed may be fine for two small goats- if your weather is good. If you live where it's very cold/rainy a lot it might not be if they don't have other cover. We have a 8x10 building with one open side for 4 goats- 3 large goats (one is still little) and one Nigerian Dwarf. They have plenty of room, but we are in Florida so we don't have super cold weather, snow, etc. Goats HATE the rain.