Tetroace wrote:A folded out 4D cube would look like 2 3D crosses fused together in their centres (making it look like a + from above) am I right?
Yes, if I understand you correctly, that would be a fair description of one of the several ways you might conceptualize "unfolding" the eight cubical sides of a tesseract.
As for the idea of cubes "passing through" each other in four dimensions, I think that terminology is rather misleading. Taking it down a dimension where you imagine a square lifted out of the plane into three dimensional space, it would simply pass
around ("over" or "under," you might say) any squares that remain in the original reference plane. Likewise, if you imagine a cube being lifted out of its original space into a four dimensional hyperspace, that cube would pass around other cubes left behind in the space, without passing "through" them in any way.
Here's another way to look at it. Imagine a smaller square enclosed in a larger one. So long as both shapes are restricted to the same 2-D manifold, they are locked together. By introducing a third degree of freedom, however, the smaller square could be lifted "out" of the plane and then placed back "into" it some distance away without ever intersecting the larger square. That should be relatively easy to conceptualize.
Now move up a dimension. You have a smaller cube enclosed in a larger cube. So long as both shapes are restricted to the same 3-D manifold, they are locked together. Now introducing a fourth degree of freedom allows the smaller cube to be lifted "out" of the space and then placed back into it some distance away without intersecting the larger cube. Congratulations! With an extra dimension at your disposal, safe-cracking is now child's play.