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It is mushrooms, essentially. This article will help:
https://www.gardeningknowhow.com/lawn-care/lgen/eliminate-mushrooms-in-your-lawn.htm

It would not have contained black walnut. But, if you use mulch every year, the soil may be depleted of nitrogen, which would stunt plant growth. You should have the soil tested to see if this has happened.

Another possibility is that the mulch was dyed, which has its own issues. This article has more on that:
https://www.gardeningknowhow.com/garden-how-to/mulch/dyed-mulch-in-gardens.htm

This is powdery mildew. Powdery mildew is caused by fungus. For more information, here is an article or two that you may find helpful: https://www.gardeningknowhow.com/problems/get-the-cure-for-powdery-mildew.htm
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

It can also be treated effectively with neem oil. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Yes, any time you leave dead material out, there is the potential for mold or other problems (such as pests, disease or fungus) to develop, especially in wet environments.

I would recommend that if you are going to leave the leaves piled up around the tree, that you chop them up with a lawn mower. This will increase how quickly they decompose and reduce the amount of time they potentially have to develop a problem.

You can also try using a weed barrier below the new mulch. Thick layers of newspaper, cardboard or landscaping cloth will work. You can lay the new mulch over the old without having to weed. The weed barrier will kill the weeds (by blocking the sunlight) and keep them from growing up through the mulch.

Hard to tell from this information, they could be many different things. Your best bet is to take some to your nearest extension service, or contact an entomologist at a local university; someone there may be able to identify the eggs.