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The plant appears to be growing well, but it could benefit from being repotted in a larger pot with a well-draining soil mix. This will provide more space for the roots to grow and improve the overall health of the plant. Additionally, fertilizing the plant with a balanced liquid fertilizer once a month will help promote growth and maintain healthy foliage. It is also important to keep the plant in bright, indirect light and ensure that it is not getting too much direct sunlight, as this can cause the leaves to become scorched. Overall, this is a healthy plant that just needs a bit of maintenance to continue thriving.
It looks like it isn’t part of the same plant so I would remove it. It’s growing well and has new growth so you might try planting it to see what happens.
Yeah, it looks like some type of vine or ivy & in my experiences. I have issues with vines & ivy running a bit wild and they tend to grow up my tomato plants choking the life out of them, so yeah, I would highly suggest moving it.  if nothing else it’s taking nutrients out of the soil that the plant you want to thrive is using. 
I would recommend to remove it. It could damage you plant