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We came up with a variation of thyme, such as creeping thyme or woolly thyme. Sedum varieties also form a dense mat like you are wanting. Here is growing information:
https://www.gardeningknowhow.com/edible/herbs/thyme/woolly-thyme-ground-cover.htm

It looks like torenia or wishbone flower. It is usually grown as an annual except in warm climates where it is perennial.

https://www.gardeningknowhow.com/ornamental/flowers/wishbone/growing-wishbone-flowers.htm

It looks very much like Amsonia Hubrichtii, a U.S. native shrub that has needle thin foliage with star-shaped light blue flower clusters in spring and golden fall color. Also called Arkansas Blue Star.

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I believe you may have honeysuckle bushes growing there and they are considered exotic noxious weeds in Kentucky.

https://forestry.ca.uky.edu/bush_honeysuckle

It may be a plum, or my best guess is a cherry plum (Prunus cerasifera), or another species from the genus Prunus. Did it produce flowers and fruit?

The upright portion appears okay, and if you want a single stem tree, you could prune off the fallen/leaning portion at the base and leave the upright.

But if you want to save the leaning portion, you will have to get in there and determine if the stem or stems are broken or just leaning due to overburdened weight distribution. If not broken you may be able to reduce some top weight or branch end-weight by pruning it back some, which may allow it to pop up into better position. That along with some thinning of excessive number of stems and you may be able to straighten it up. If there are broken stems it will best to remove those at the base.

https://www.gardeningknowhow.com/ornamental/trees/cherry-plum/cherry-plum-information.htm