Can something appear from nothing? If no, how did our universe appear? If yes, doesn't this violate the conservation principle?

Yes, I believe that Allah created everything out of nothing because he is The One and the Only Creator of the universe but humans can't do this, they only could make things from other things  

I agree with M's Rima answers, about that Allah able everything from nothing . But human not able that. 

The answer is yes, and it do not violate the conservation principle. The phenomenon is known to physicist as Quantum fluctuation or Vaccum fluctuation which is the temporary appearance of energetic particles out of nothing, as allowed by the well known uncertainty principle, for instence:  a particle pair (electron/positron) can pop out of the vacuum during a very short time interval. So, the lower the energy of the particle pair, the longer it can exist.The same concept apply in cosmology. It is known as the zero-energy universe hypothesis which proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity.a gravitational field has negative energy. Matter has positive energy. The two values cancel out provided the universe is completely flat. In that case, the universe has zero energy and can theoretically last.