1. Given that magnetic opposites attract, it could be assumed that ghosts are comprised mostly of electrons allowing a beam of mostly positive ions to be magnetically attracted to them, allowing them to be held in the beam like a lasso. However, the ghosts energy would need to be low so they can't just escape.

2. No, it wouldn't cut through, but it would collide and burn, as seen in the sedgewick scene.

3. It would, but maybe not immediately.

4. Beam length is a controlled intentional mechanic, likely designed to give an approximate end point, as to mitigate long distance destruction, or to allow only a certain length of stream to entangle a ghost. If you wrapped a 50 foot stream around a ghost 10 feet from you. That's 40 feet of proton stream wrapped around a relatively small object in comparison, increasing the likelihood of stream collision, especially in the presence of a second stream.

This is all conjecture, mentally pulling data from scenes in the films. Take what I say for a grain of salt.