I was simulating a few thousand years of solar system orbits with Sky View Cafe and noticed that the orbits change a lot during a few millennium.

Pluto (the former planet) and Neptune's orbits gets very close and they cross over at times, so :

Assuming we give it billions of years, is it possible for Pluto and Neptune to crash?

Is our measurement of positions/speed accurate enough to predict such a crash?

The gravity might also play a role and prevent the two from crashing, how would that work? Can we predict that it would "never" crash?

And finally if they do crash what can we expect? Would earth be in any danger?