I don't know about the straws, but yes, you should remove the plant if it is melting. It will only pollute the water. Do you know what type of plant it is? Do you want to try live plants, or are you going to replace it with a fake plant?
Could you get a picture of the plant? It sounds like it might be anubias, but it could also be an Amazon sword, which are easier to kill if you don't have the right lighting. If it is anubias, you might have some die-off of leaves, but it could still come back.
If you decide to go with plants there are a ton of topics that can help you get in the right direction, and feel free to ask any questions.