Our son is 15 now, but we took him to Japan a few times when he was a baby or toddler. I think your trip is very feasible.
1) Should be no problem. It sounds like she will eat almost anything, which is terrific - many kids don't. Our child had a lot of rice and hot tea, since he didn't like foods that were mixed together. We sometimes bought raw fruit and veggies in stores, and he was willing to eat those as long as they weren't touching any other foods! He also liked kara age, which is fried chicken, and some types of sushi (cucumber rolls, eel).
Milk is not as common in Japan as it is in the West. You may be able to find it in hotel restaurants for breakfast (for cereal), or in grocery stores. Your daughter might like a yogurt-based drink called Yakult, which you'll see in convenience stores, stores in train and subway stations, and vending machines. By the way, when our son was little, he LOVED pushing the buttons on vending machines.
2) Don't try to do too much. Pick a few places where you can spend several days, and leave time for naps and playtime. If you can, try not to take the train or subway during rush hour because they are more crowded then.
3) Ryokan and minshukus are Japanese-style accommodations (ryokans tend to be fancier, and minshukus are cheaper and more bare-bones), which means you'll sleep on futons. We often slept family style on futons. Plus they may include breakfast, maybe dinner too, in their prices.
