Is it realistic to have a livable planet with a quarter the size of Earth, but with the same gravity?

So in theory, I would want this planet to have the same everything as earth besides the radius (and anything that affects how radius plays into gravity). I know the density of this Planet X would have to be quite high based on some quick number crunches. But I'm not sure how realistic this would be. Would the planet be livable? How different would the temperatures of the planet be? Could it be mostly water (how does water affect the density)? Is there a way to have that high a density core?

Realistically how close could an average moon be to this planet? Could this planet have rings?

I have a fair idea of how planets work but not enough knowledge to actually know how realistic this might be.

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Is it realistic to have a livable planet with a quarter the size of Earth, but with the same gravity?

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