I have completely redone my question. I doubt users in Math Stack Exchange will answer. If the question is unclear/off-topic but you understand, and know how to improve it, is it possible to re-edit the question?
The only person who helped is @WillieWong and he is on MathOverflow. He understood what I meant by reading the original questions. He might be able to answer this last one but in one of the comments stated: "Now I am really done". I am not sure if he understands everything I require.
I apologize that my posts are so hard to read. I apologize my questions lack rigor but they can become rigorous with help. They are getting better every time. It just seems no one willing to continue helping.
Edit: I would also like to know why this is unclear.