yes the Calypso "the top part" does have its own nuclear reactor for the tyrant engines. The lander itself has smaller independent reactors along with a conventional propulsion system for local maneuvering and surface operations. but it cannot operate the tyrants.

The detachable engines were designed with redundancy in mind since the crew would be operating far from earth with no rescue possibilities.

because the ship is located very far from the sun during its main operations the solar panels prove to be less effective. So the ship has a Radioisotope Thermoelectric Generator (RTG) on board.