Was watching Rick and Morty on the Season 3 premiere and they have that very small planet that the family goes to to escape. The planet is humorously small in that it is noticeable round while walking. The planet also apparently has animals and breathable air for humans. At one point, Rick goes to the South Pole of the planet and goes into a cave that takes him to the core of the planet which is shown as being smaller than him, from what I remember and what it looked like.

Could a planet like this actually exist with all of these features, only being a few acres in size, at most? Would a breathable atmosphere be possible? Would a core be present at all?

To put it in more realistic terms, the planet would be the size of Manhattan Island in New York City but folded to be round.