You won't be able to grow most of your list.

Your burlap sack idea will not work because it will drain too much and dry out too fast and the plants will not get enough water.

Many herbs like dry soils though and do well in pots. the mints, basil, parsley, thyme.

Broccoli is a heavy feeder that doesn't like containers, though you can make it work.

I would cross onions and carrots and garlic off just because they're not high value crops, and you don't have a proper garden to plant them in.

The lettuce and the spinach are early season crops, they do well before the weather gets warm. You can do them in containers, though they will need extra water if they get a lot of sun or get hot (those leaves respirate a lot of fluid).

Tomatoes are of course famous for containers. Big self watering containers especially, google "earth box" or "grow box"

If you're really really diligent about watering you can grow zucchini, squash, melons, etc from containers. But you need to water a ton, those huge leaves really need moisture. The plants will tell you when you need to water though by drooping obviously.