I'm trying, for example, to make a simple 3D box with the use of paths. I know how to make the paths, I also know how to make them act as one path (intersect). But to make a 3D box I need to connect the different sides of the box seamlessly. I thought I could do this by simply snapping the corner points of each side together, but I don't know how.

So my question then is, how to I snap two points of two different paths together?

don´t think u can do that, but what you can do is one path and then just split it with a line...... hope that helps.

With which tool can i cut the path in half then?
I want to be left with two seperate paths, lying against each other, not one path with al line crossing them.

can you post an image of what u want? but you can have as many paths as you want, you can make to separte boxes and distort them, or in photoshop you have the same path tools as in ilustrator, such as the pen tool, select, add node, remove node and so on.....
hope that helps
vince