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Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/trees/tgen/what-does-a-dying-tree-look-like-signs-that-a-tree-is-dying.htm

It is borers. I would recommend neem oil to treat the plant. Neem oil is a systemic pesticide, which means the tree actually absorbs it and it flows through the tree, getting even pests on the inside of the tree. If this tree is important to you, I would also recommend having an arborist look at it.

I would leave them alone. Typically when a tree grows back from the roots like this, it will grow in a bush form forever. Yours will likely do the same. You can encourage more bushiness by trimming the top a bit and this will force the branches to grow outward even more.

I am going to refer you to a very excellent article on bark splitting from Cornell University which discusses the possible reasons this occurred (various environmental factors). This split in your tree is not likely to be fatal but the article will outline things you can do to encourage the natural callusing process that the tree will undergo to close that split.

(Cornell University PDF – bark splitting on trees): https://bit.ly/1KEmrRn

You will want an American Linden tree. If possible, look for the 'Boulevard' or 'Douglas' cultivar. These will be the most tolerant of your conditions.

Was a weed and feed product used near your tree?
Linden trees are sensitive to herbicides.

Have you inspected the leaves? Look for any signs of disease or insects.
Weather stresses can cause a Linden to loose leafs also.

https://www.gardeningknowhow.com/ornamental/trees/linden/linden-tree-information.htm