The possibilities are there. Space travel is possible, but not anywhere near the speed of light. One could never reach that sort of speed due to the relativistic mass increase. To get something the size of a space ship to even half the speed of light would require a huge amount of energy. More than could practically be created in this day and age, but then people are always finding new ways of doing things. As for transporters, they will probably never become a possibility for one reason, the Heisenberg Uncertainty Principle. This is one thing in the universe that I am sure even the most brilliant scientist will not be able to find a way around. The problem is not in locating the object (i.e. an electron), but that its properties, such as position, momentum and direction are intrinsically indefinable, that is, the electron itself is 'not sure' of what its properties are!
Space travel at speeds lower than the speed of light is not practical due to the long distances involved. Even if we could reach light speed, relativity suggests that if we travel that fast for extended periods then time would travel more slowly for us. The result being that if we were to travel to a distant star and back, the time it takes may seem to us like a few weeks or years, but on Earth millions of years would have passed!!
I think that for now we will just have to put up with travelling at a mere few of hundred mph in conventional transportation.
So it seems that we will never know any of the 'Star Trek' technology. However,
I like to think that the answers there, it is just that we may not be clever
enough to find them! The truth is out there!!