Upload a photo? of what? and for what?
No. Use slaked lime or hydrate of lime (calcium hydroxide) which comes in a white powder. Here is more:
https://www.gardeningknowhow.com/garden-how-to/info/diy-bordeaux-fungicide.htm
What is it and what should I put on them?
The first photo looks like a leaf spot fungus. Here is more:
https://www.gardeningknowhow.com/plant-problems/disease/plant-leaf-spots.htm
The next two photos look more like bacterial leaf spot (halos around the spot):
https://www.gardeningknowhow.com/plant-problems/disease/bacterial-leaf-spot.htm
Your article states there is no remedy for white mold, so my garden is doomed, I want to cry! After clipping back my plant what can I do for the soil to kill or discourage mold growth?
Does your whole garden have it or just that spot where you cut back a plant? You can always solarize the soil to kill pathogens. That entails covering the area with clear plastic and weighing the edges down with bricks. It takes several weeks with sunny days. Best done in summertime. If it's not too large an area, you can remove and replace the soil. Where you cut back a plant you can treat it with a fungicide to see if that helps. However, the article says it's best to remove infected plants.
https://www.gardeningknowhow.com/plant-problems/disease/white-mold-on-plants.htm
https://extension.umn.edu/plant-diseases/white-mold-garden#use-resistant-plants-1783162
My dog rolled in this, it was covered in flies and other flying bugs. It smells so bad I almost vomited.
It could be. Here is more information about it and other things in the lawn with an odor.
https://www.gardeningknowhow.com/lawn-care/lgen/black-substance-on-lawns.htm
https://www.gardeningknowhow.com/ornamental/fungus-lichen/removing-stinkhorn-fungi.htm
https://www.gardeningknowhow.com/plant-problems/weeds/how-to-kill-stinkweed-plants.htm
It is initially puffy and almost sticky, sort of looks like vomit. I’m guessing that it is a fungus of sorts but it only appears on my mulch. Is this harmful to animals and plants?
It is a common mold that mulch tends to develop now and then, which indicates it is decomposing. You can ignore it if you want. Or spray some vinegar.
Can I spray plants that have fungal problem. With vinegar and water.
I would opt for a safer fungicide. While vinegar is an effective fungicide, it is also an effective herbicide. Do expect the top of any plant sprayed to die off.
https://www.gardeningknowhow.com/garden-how-to/info/use-vinegar-in-gardens.htm
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
I've been watering at night and in the morning because it's been so hot
This is a collection of fungal infections. Though They will need water during hotter periods, they will need to dry out down to 5 inches or so, as well. This will be to avoid root suffocation and infection. After this, I would recommend letting the soil dry down to a few inches between waterings, and add shade during the hottest part of the day, if possible.
A fungicide will be necessary as well. These articles will help:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
https://www.gardeningknowhow.com/plant-problems/environmental/plant-care-during-a-heat-wave.htm
https://www.gardeningknowhow.com/garden-how-to/info/watering-during-heat-waves.htm