The 1st and 3rd photos show a vine known as wintercreeper or euonymus vine. The botanical name is euonymus fortunei. This is considered an invasive plant, which means it grows aggressively in wild and natural areas, damaging the native environment.
We recommend that you kill it. You can do this by cutting it off at the base. It helps to quickly paint or spray an herbicide on the fresh cut. Use an herbicide containing glyphosate or triclophyr. These are "systemic" herbicides that go down and kill the roots. Re-cut and re-apply to any suckers that may come up. Another tip to kill the vine is to smash the fresh cut before you spray, making it ragged and harder for the vine to heal.