When measuring the jitter, the jitter value should depend on the pll setting.
The datasheet says you get the minimal jitter when setting the pll's vco frequency close to the max 1596MHz, with the dividers set such you get the CPU clock.
Yes, and note it will also depend on what else the Pico is doing.
Being an active digital device, the ground /supply noise will affect the oscillator.
For lowest jitter, I've seen a (different micro) PCB changed to external clock, as they found digital pins near the XIN pin, had a measurable degrade effect on PLL.
Of course, low noise power supply also helps.
A quick search found a couple of reports of people feeding CMOS oscillators into XIN
I have a pico-zero here (linear voltage regulator), 3 crappy scopes, I doubt any of them is suitable for for such a measurement. That would require a timenut like equipment, my bet.
A simple XOR gate and low pass filter into a audio sound card could give you some idea of close-in jitter.
If you use an external low jitter oscillator, that can feed one side of the XOR, then various PLL settings can compare on the the pin.