1. Seam edges can't be deleted, you can only hide it. because it's the curve which forms the sphere.
2. Your sliced spheres are sliced vertically. Short lines are not seam edges anymore, they're regular lines because resulting pieces are calculated differently than the sphere thus this script is not working.
3. if you sliced them horizontally, script would work.
4. yes they return after slice because script hides it only visually. :(
5. yes this script affects whole scene. :(