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It sounds like a pest of some kind is affecting your shrub, such as aphids or scale. These pests are both treated the same with a pesticide. I prefer neem oil myself because it is safe for people and pets and also addresses other issues the plant may have. Here is more information:
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

You don't have to, but since this is their first winter, it does not hurt. The first winter a plant goes through after being planted is always the most dangerous for the plant because they are only marginally established and sometimes this can make it hard for them to survive the stress of the winter. Covering them with burlap and/or mulching the base heavily will help to protect your investment. After the first winter though, most azaleas do not need to be protected.

I would take a look at the roots. You may have some root rot. It may also be a fungus attacking the azaleas, so you should go ahead and treat the others with a fungicide.

It sounds like you have both aphids and sooty mold. Sooty mold is a common side effect of aphids. These article should help you:
https://www.gardeningknowhow.com/plant-problems/pests/homemade-aphid-control-a-natural-way-to-kill-aphids.htm
https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm

This may be lichen. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm

Wait after blooming has stopped before pruning your azaleas. This article may help you if you have not read it: https://www.gardeningknowhow.com/ornamental/shrubs/azalea/pruning-azaleas.htm