I went in for a closer inspection in an attempt to grab a closer picture of a bud, then it's struck me... there's actually a "parasitically" attached bigleaf magnolia growing out the side of the tree. So the main tree must definitely be a beech. I agree with the laurel assessment, but the validation confirms it. Thanks again!

Likely non-native shrub honeysuckles which can be invasive. I would encourage you to remove them.

It looks to be one of the mugos neglected for a couple of decades. Cut the ropes and cut it down to the ground or you'll have something akin to the ex-planet Pluto to contend with. It won't regenerate - you've got no needles beneath the rope line to work with... in the event you considered it. If you don't need the space to plant something else, I wouldn't bother trying to dig it out. A hand ax will take out what's left of the branch stumps a bit below ground level.

I will investigate that. Thank you.