I'll save people the effort and point out that the only relevant things (to the given questions) the entertaining video shows are a proper klein bottle and the

I'll save people the effort and point out that the only relevant things (to the given questions) the entertaining video shows are a proper klein bottle and the nature of projection into 3D. In 4D, klein bottles don't self-intersect, just as mobius strips don't self-intersect. It does not cover the question of putting oneself inside a wall or how to go around 4d objects, and the projections show detail that a 4d person would not see.