Redefining habitable zone for advanced Terran animals

[AstroChara]

The Earths core is able to rotate in this manner because it is still hot enough to remain liquid. The core of Mars lost too much heat and froze solid eons ago. Like you say, our planets superheated core may be tied to the Theia impact which formed the Earth and Moon.

Every inner planets' cores are molten. Yes, all of them, even Luna.

The reason Mars and Venus lack a magnetic field might be due to the temperature difference between the inner core and the mantle being too low to generate convection, which is probably required for the dynamo that generates the magnetic field...
For Luna, it's probably both that and the fact that its liquid core is, well, way too small. It probably once had a functioning magnetic field though.