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Removing the roots is not advised, but you should be able to work around them by adding soil and plants as you want them. This article will tell you more: https://www.gardeningknowhow.com/ornamental/trees/tgen/exposed-tree-roots.htm

This article mentions various points of Japanese maple care that you might want to check on: https://www.gardeningknowhow.com/ornamental/trees/japanese-maple/japanese-maple-care.htm
This article covers leaf scorch, which can result in leaf loss on one side of the tree: https://extension.missouri.edu/p/G6881
In order to find out what is affecting your tree, you should seek the advice of a horticulturist or university botany dept.
Pale green crusts on the branches sounds like lichens, which are not harmful. This article tells more about them: https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm

The grey growth is likely lichen. It is not the cause of the trees problems, but rather a symptom. They tend to attach to trees that are sickly and unhealthy. This article will give you more information: https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm In regards to what may be wrong with the tree, I would take a look at the roots. You may have some root rot or the tree may need to be repotted. It may also be a fungus attacking the tree, so you should go ahead and treat the tree with a fungicide, which will actually also get rid of the lichen.

It is definitely stressed, as lichen normally only hangs out on stressed plantings. Tree suckering at or around the base is another sign of stress. It is difficult to say what exactly could be the stressor - may be a lack of water, could be insect pests or even disease. It might be a good idea to call an arborist or contact your local extension office for advice. Someone that can come out and look at the trees could be of more help. Here is a link to help locate your county extension agent: https://www.gardeningknowhow.com/extension-search

There isn't anything special needed to add but I would allow it to sit for a while before placing around plants. If it's too fresh, you run the risk of burning the plants, as the mulch will still be too hot. Generally, it should be allowed to age for about 1-3 months (or more), depending on how much you have.

Maples are notorious weed trees. Single stem young saplings can simply be cut off at ground level and they will die. More established saplings that have already branched will need to be cut off and their cuts painted with Roundup to prevent them from regrowing. This article should help: https://www.gardeningknowhow.com/ornamental/trees/tgen/weed-trees.htm