I'm not sure what that wall does, but the easiest way to find intersections, roots, etc. of Bézier curves is to use their convex-hull property and recursively bisect them. The convex hull property is that the curve is within the convex hull of the control points. So given two Bézier curves, if their convex hulls don't overlap, then they don't intersect. If they do, then split them both in half and see which of those Béziers' convex hulls overlap. Recur until you reach a tolerance, then just approximate the curves by a straight line and find the intersection point (or basically equivalently, just use the average position of the control points, since at that point the line is pretty much straight).
