Star Trek

Terra-forming is already theoretically possible and couuld be done with current technologies. However, the cost is so large as to be immeasurable. we Do not have the technology to transport the the needed equipment to a suitable planet, and the process would take millenia.

I am not familiar with "Start Trek"

Science fiction is fiction, but it often gives scientists and inventors great ideas.  I believe that even if we are unable (yet) to accomplish many of the technological developments that appear in movies, series and books, the attempt to exceed our current limitations is what expands our minds and our cultures.  Otherwise, we would have remained like the Neanderthals.

IF we were to find an FTL drive that works, we would need to first invent Inertial Tampers. Its like a car, you could build the engine, but you need tires, seats and windows... Oh, and brakes.

Faster than light travel has been proven to be possible because of the neutrino that was observed at CERN at arriving at its destination before the photon did.