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It sounds like either a nutrient deficiency or a drainage problem. Have your soil tested, then amend the soil accordingly and make sure that the plants are not in standing water

It sounds like a fungus, likely Leaf Spot Fungus. This article will help you:
https://www.gardeningknowhow.com/plant-problems/disease/plant-leaf-spots.htm

This article has recipes for homemade sprays:
https://www.gardeningknowhow.com/special/organic/natural-home-pesticides-organic-garden-pest-control.htm

I like neem oil myself. You have to buy it, but it is organic, safe for people, pets and good bugs and very effective. Here is more information:
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Azaleas love acid, and lemons are high in acid, so they would make good fertilizer. I would not put the lemons on the ground as is though, as this could attract vermin and possibly burn the soil. Instead, I would compost them first before applying them to the azaleas.

If you have had a rather cold winter, than this will do this to azaleas. They will be fine and will regrow new leaves in the spring.

It sounds like the tree has sooty mold, which is actually an indicator of a pest infestation. Many times the pests that cause sooty mold are too small to see, but they can be damaging. I would recommend treating the plants with neem oil. This will treat both the pests and the sooty mold. Here is more information that may help:
https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm