Well you can forget number 3. If the area is in full shade all the time, it is not a spot to grow vegetables. But there are plenty of things that will do fine with four hours of sun a day or constant dappled shade. In fact if your climate is hot and sunny during the growing season, all the cool weather crops will benefit from the shade. That would include:
Beets, swiss chard (I only fairly recently discovered those are actually varieties of the same species, just one is cultivated more for the root and one for the leaves, but we also eat beet greens.) All the brassicas can handle shade pretty well and don't like the heat. That includes broccoli, cauliflower, brussels sprouts. All the salad stuff-- lettuce, spinach, kale, etc. Peas.
Some that are a little more borderline, but might do ok in the 4 hrs sun are bush beans, potatoes, onions, garlic.
And of course mint will grow pretty much anywhere. Put it in the full shade area, that will slow it down enough that it won't take over your yard!