How is it possible that an LC Oscillator create a sine wave?
1) ... the capacitor, since there isn't a resistance is shorted, so how can it create a sinesuoidal wave?


The inductor might have a very low resistance (or zero in the ideal case) so it presents a short-circut for DC but not for AC. The thing is that it's not DC - the current is changing.


  2) How is is possible, taking on the capacitor full charged, and without a resistance, that this circuit swinging will create a sinusoidal wave, ...


The energy is sloshing back and forth between the capacitor and the inductor.