If the LHC test energy levels present just after the Big Bang, is it possible to test higher energies? And, if so, would that be relevant to anything in this universe?
 A: I think you may have understood what is meant by "just after the big bang".  According to the laws of physics as we currently understand them, the temperature in the immediate aftermath of the Big Bang was (roughly) inversely proportional to the square root of the time since the Big Bang:  $T \propto t^{-1/2}$.  In other words, it was about $1.3 \times 10^{10}$ K one second after the big bang;  $1.3 \times 10^{11}$ Kelvin 0.01 seconds after the Big Bang;  $1.3 \times 10^{12}$ Kelvin 0.0001 seconds after the Big Bang;  and so forth.  Extrapolating, you can find a moment some tiny fraction of a second after the Big Bang where the temperature was arbitrarily high.   And the hotter the Universe was, the more energy the particles had at that time.
So when people say "the LHC is giving particles energies not seen since the moment after the Big Bang", what they really mean is something like "since $10^{-3}$ seconds after the Big Bang" or something like that.  A particle collider with even more energy would be able to probe up energies that only existed $10^{-5}$ seconds after the Big Bang, and an even more powerful one would be able to probe energies $10^{-10}$ seconds after the Big Bang.  
