1. First of all, the crystal oscillator you are talking about is a quartz crystal oscillator.
2. "The peak-to-peak value is 1V, which means the value from negative peak to positive peak is 1V, so it is actually ±0.5V." This understanding is incorrect. From the poster's description, it should be understood that the output waveform of the quartz crystal oscillator is a sinusoidal waveform; the amplitude is 1Vp-p, which is 0.707Vrms. Maybe the author wants to say that the half-cycle peak value is 0.5V, but he cannot describe it this way.
3. Some crystal oscillators have built-in voltage stabilizing circuits, so 5V and 3.3V are optional. This is to facilitate users to install it in different power supply circuits.
4. As for the 0-1V sine wave mentioned by the poster, I have no idea what it means.