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Yes, I would advise that very technique!

This can be very hard to do, as many of them look almost identical. It appears to be a type of red oak, which will mean that it should bear acorns around September. Again, this is my best guess, and will be very hard without being able to test its genetics. This can be expensive, and not worth the hassle.

This sounds like it could be Oak decline.
This article has more information.
https://www.na.fs.fed.us/spfo/pubs/fidls/oakdecline/oakdecline.htm

I would also suggest you speak with your County Extension about the issue in your neighborhood.

Here is a link to help you locate your nearest office.

https://www.gardeningknowhow.com/extension-search/

This is a fungus of some type. Some fungus can be of no concern, though it can be symptom of bigger problems.

You may want to have the tree examined by a qualified Arborist.

You actually appear to have had a Maple Tree.

I cannot id from your images, the variety.

Visit your local garden centers and nurseries to look for a suitable replacement.

https://www.gardeningknowhow.com/ornamental/trees/maple/growing-maple-trees.htm

Shading as well as root density and competition for water and nutrients may be responsible for the suppression of grass. The same conditions will make it difficult to grow other plants.
Consider mulching the soil surface with wood chips or commercial mulch material instead of using river rock. The mulch will have a more beneficial effect for the soil fertility and the trees.