I'm afraid that's nowhere near enough sunlight for any food plant. You could grow some shade loving flowers or ornamentals, but not vegetables.

Also gongura is a shrub that gets at least 5' tall, so it isn't something you can grow in a pot on a balcony.

You can buy okra in the grocery stores in season so I wouldn't worry to much about trying to grow Okra.

You could grow eggplant and peppers and tomatoes inside in containers with a LOT of light (you'd need to set up an area with a lot of fluorescent shoplights). This can be done but it's not something I would suggest to a novice gardener. The National Gardening Association sells some 4 light fluorescent plant stands but they are quite expensive (4 fluorescent bulbs per shelf, the MINIMUM to even try indoor gardening).

http://nga-gardenshop.stores.yahoo.net/

Also a good source for information about gardening in general, they have an online tutorial about container gardening up right now. It's really oriented towards growing outside in containers though.

http://www.garden.org/home

Have you looked into the possibility of community garden plots? Many cities have community garden plots you can rent, or they should know of any gardening societies that provide this service.

I'm afraid none of the things you want to grow will grow well on a shady balcony. Also the beans are vines and require a lot of space in full sun to grow and bear, you couldn't grow those indoors at all.

If you want to try indoor gardening I would start with a small fluorescent light setup with cilantro, mint, or other small plants so that your learning curve isn't too horrendous. You could set these plants out on the balcony for the 1 or 2 hours of light they could get there but they need more light, you would have to bring them back indoors and keep them under lights for at least 12 hours a day.

Check the following forums on this site for information about growing indoors:

Growing Under Lights
Hydroponics
Container Gardening

Also check out Gardenguides.com's container gardening forum.

Here is a link that might be useful: Garden Guide Forums