Hi Shanti, good for you! I have a traditional garden, so my advice may not be the best, but I imagine you would want to avoid two types of vegetables:
1.) First, I would avoid plants with a deep tap root. Parsley, cilantro, and carrots have tap roots and may struggle in shallow soil. Potatoes and leaks require trenching and may also be difficult to grow in shallow soil - but onions, scallions, and chives would work fine!
2.) I think you might also want to avoid plants with a 'sprawling' habit, simply because you have so little space. The only one on your list that fits that description is cucumber (although with some difficulty, they can be trained to grow upwards). Broccoli is also a very large plant.
In summary, I think you would do very well with the leafy greens, chives, onions (scallions are very space-efficient), peppers (which would love your climate!) Cucumbers and broccoli would thrive, but may take up more space than you want to spare. (Eggplants and bush beans love the heat as well and are quite compact!)
I hope you will check back after your garden is growing and tell us what is working!! Hopefully you will also get advice from someone with more container gardening experience than I have.
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