Technically, anything can be grown in a container. What you have to consider is how much soil each plant needs based on the size of its mature root system, how much sunlight each plant needs to produce fruit, and how much each plant requires in the way of water and nutrients, and finally, how large each plant will be at maturity. Then you have to set about fulfilling the needs of each plant.
In general, root crops aren't very satisfactory as container plants, because of the low yield in relation to the space required. Melons and squash aren't usually grown as container plants because the vines spread over such a large area. Sometimes, smaller species of melons can be trellised, but it will require some extra work.
A standard tomato plant, regardless of the size of the fruit it produces, needs at least a container the size of a 5-gallon bucket, and larger is better. If your patio space is limited, consider growing one of the dwarf varieties, such as "Patio" or "Tiny Tim". They will do well in smaller containers of 2 to 3 gallon size.
All tomatoes are heavy feeders and need a lot of water. The fertilizer needs will be different, depending on whether the plant is in the growth phase, or mature and ready to fruit. They also need about 6 hours of full sun each day.
I've used tomatoes as an example, because they are popular and they're on your list. If you can provide for the sun/space/water/food needs of tomato plants, you should be able to grow a variety of other plants, as well. Going into detail about all of the plants on your list would require a book.
Review the space and sunlight you have for mature plants. Let us know the size of your balcony and which direction it faces, as well as whether it's open or covered. That information will help us help you. You may need to pare down your list a bit before going into all the details of what each plant will need in order to thrive.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams