Newbie needs some identification

I'm a newbie of course but I bought a green leather and a purple pulsating Xenia from a person on this forum and he gave me this green stuff. I think he called it green polyps, but my memory is horrible. Also the tan thing growing on it, is it a mushroom? I also got a mushroom from him and its shaped like this but different color and the one in the pic looks really thin and soft. In the last week it has doubled in size. I don't want it to take over the green stuff or anything else. Any help identifying this stuff would be greatly appreciated.

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