How can I predict space directions? Did the Neptune and Pluto trajectories ever cross or was it a mere reclassification? Do studies say that I can predict an intersection between 2 trajectories  or movements based on data now? Do I have to consider at least 3 solid or larger space bodies moving in a way like the 3-body problem?
If you project the orbits onto a plane, for example the plane of the ecliptic, the projections will cross. But that's only because you're looking at a 3D problem in 2D. If you look at the orbits in 3D, you'll see that Pluto's orbit is highly inclined (17º) from the ecliptic, so it never actually passes through Neptune's orbit. Each time it seems to cross (in the 2D view), it's actually well above or well below Neptune's orbit. Pluto and Neptune never come closer than about 17AU.

At least for now. Minor perturbations over tens of millions of years may change that. Or might not. Pluto and Neptune currently have a 3:2 resonance, and such resonances tend to be stable.

You might want to look at http://en.wikipedia.org/wiki/Pluto, especially the section "Relationship with Neptune".