Star Trek Universe. Is it possible?

Out of all literature and television stories ever invented, Star Trek has to be one of the most captivating of all. The question on my mind is whether or not all the stuff in Star Trek from warp ships, Q's and the Omega Particle, are these things possible in our universe? Can warp ships be achieved, will meet beings that fit the definition of God? Will we ascend in the ranks of the galaxy and create a society like the Federation?