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Yes, placing a layer of mulch on top of the soil, whether it be pebbles or wood chips, will help keep moisture in the soil. You can also place the plants on a tray filled with pebbles and water, and this will help increase the humidity around the plant.

For barrels, you will just want to make sure that there are drainage holes cut in them if you use them to grow plants in. This article will have some other tips: https://www.gardeningknowhow.com/special/urban/balcony-vegetable-garden.htm

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. Fill the tank with water to check for leaks, using epoxy sealant to fix those present. An inch of small gravel or aquarium stones in the pot bottom ensures adequate drainage. Top with another inch of charcoal chips and add a layer of peat moss followed by a layer of potting soil mix (two parts potting soil with one part perlite or coarse sand). Plant your herbs and keep the soil moist, but don’t overwater.

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There are several different options available to you with regard to your question about window boxes. It appears you only benefit from morning sun, so a mix of herbs and some perennials that like partial shade would be a good choice. You probably want to consider using window boxes made from light weight plastic materials, that would be much easier to move even with the addition of soil and plants. Many look like wood or terra cotta. This article may be helpful to get you started.

https://www.gardeningknowhow.com/edible/herbs/hgen/growing-herbs-in-containers.htm

This article should help: https://www.gardeningknowhow.com/special/urban/creating-your-own-rooftop-garden.htm