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This article should help: https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-sucker-removal-and-tree-sucker-control.htm

Undiluted Round-up will help kill the roots. You will need to wound the roots (normally, people cut the suckers down and use those wounds) and then paint the undiluted Round-up on the wounds. The bigger or more wounds you paint, the better.The roots will suck the Round-up in and it will kill them. You may have to repeat the process a few times to fully kill the roots if the root system is still strong.

Your problem sounds like lichen, which poses no real threat. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm

Yes, they will.

It may be suffering from transplant shock. This article will help:
https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

Younger dogwoods will take longer to bloom. normally they need a year or 2 to be mature enough. But you mentioned that it is planted in the yard. If you fertilize the lawn, it is possible the lawn fertilizer is keeping it from blooming. Lawn fertilizer is high in nitrogen, which inhibits flowering.

This article will help as well:
https://www.gardeningknowhow.com/ornamental/trees/dogwood/dogwood-tree-not-flowering.htm

It is pretty difficult to over water a tree. As long as it is not in standing water, you can give it more water.