Yes, you can adapt a nuclear reactor to work in space, and there have been programs in the past that aimed to do just that. Presently there are no NASA missions funded that utilize nuclear propulsion. There are several interesting possibilities for future missions, across great distances, that can be enabled only by high-energy propulsion systems using nuclear energy, or something at least as energetic. An example would be crewed missions to Mars - such as you are working on. In case the nation should ever decide to pursue any of these missions, NASA has a small research effort looking for avenues to insure their accomplishment in the safest, most reliable and least cost way.
Nuclear propulsion is a possible avenue.
An RLV is a Reusable Launch Vehicle, in contrast to an ELV, or Expendable Launch Vehicle. The Space Shuttle is a partially reusable launch vehicle, inasmuch as the External Tank is expended during every flight, while the Orbiter and Solid Rocket Boosters are reused. Question I work in the manufacture of aluminum alkyls. I think it's what is seen squirting out of tubes below the main engines at liftoff. I've heard it assures ignition.