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Yes, as long as they have similar water needs. For example, basil and petunias would be good, but I would not plant rosemary with petunias, because rosemary likes less water while petunias like more. Rosemary and marigolds or geraniums would be good, because those flowers can tolerate less water.

As long as there is adequate room for root growth and good drainage, most herbs do not require anything real deep—at least 4-6 inches should suffice. This article will help with growing herbs in containers: https://www.gardeningknowhow.com/edible/herbs/hgen/growing-herbs-in-containers.htm

It sounds like they have a fungus. Treat the plants with a fungicide and this should help clear it up.

When growing herbs indoors in a container, the most important thing to remember is to provide a growing environment of nutrient rich soil that has good drainage yet holds moisture. I would recommend placing a plastic liner inside before adding plants or even choose a small plastic pot that will fit inside the metal container. This article should help as well: https://www.gardeningknowhow.com/special/containers/choosing-containers-for-potted-environments.htm

This article will help you:
https://www.gardeningknowhow.com/garden-how-to/seeds/preventing-white-fluffy-fungus-on-seed-starting-soil.htm

It is likely residue from your water. Minerals and chemicals in your water are left behind when the water evaporates, which can look like a chalky or powdery residue. It normally isn't a problem unless you have a water softener, which means that you will have water that is higher in salt and that salt will be building up in the soil of the plant, which will eventually harm it.

If you do have a water softer, I would recommend switching to filtered or bottled water or rain water for watering your houseplants.