1 and 2) It was clearly established that Mesmero was no match for Phoenix Force Jean:
https://2.bp.blogspot.com/l2Y-GRanFR...hBUUkuuF=s1600
https://2.bp.blogspot.com/KM-IhuIFEt...qRu7cmBb=s1600
If he could overpower Phoenix Jean, then he would have been able to work out his pervert desires with her.
Also, he used Phoenix Jean to get control over Storm:
https://2.bp.blogspot.com/m-LGUBK82f...oRpscTmN=s1600
Notice how he states that he's using Phoenix Jean's powers to supercharge his hypnotic abilities:
https://2.bp.blogspot.com/4dkHraIQlH...s6Ra5r6C=s1600
So, it was the combined power of Mesmero and Phoenix Jean that took control of Ororo, and this was before Storm's willpower got the huge upgrades starting in Uncanny X-Men #151-152.
So, there's that argument taken care of. No need to bring up Storm/Mesmero anymore since Ororo is not relevant to this discussion.
3) Regarding your Rachel comment, nowhere does it state in canon she is susceptible to mind control because of her Ahab days. You are making that up. Rachel just loses to other psis because she's not a good telepath. That's all.
4) Shadow King can't operate consistently on the physical plane because he is a psychic astral being without a physical form. This has nothing to do with power levels. Also, when he took control of billions of minds scattered across the globe, he was not being amped up by anybody. He did that completely under his own power and stated that Xavier would have been the only possible threat to him. Also, in the Muir Island Saga, he didn't match Xavier, he DWARFED Xavier.
5) The issue stated if Rachel continued like that, she would have hurt herself. So, yes, she was fine at that time, but would not have been if she had kept going for too much longer. Again, if a telepath has a global reach, that means they can scan for minds across the planet. That would also mean they could sift through those minds within their global range. Cerebro does make the feat easier and faster because it amplifies their powers as you admit the device does. We are going to have to agree to disagree on this. I feel like you don't want to accept what is really common sense on this issue because you are trying to find a way to validate Rachel given her horrible track record when she is pitted against other telepaths.
6) Emma did not win by emotionally making Rachel give up. Rachel did all she could to try and win that fight, and failed miserably. When she saw that she was clearly out-classed by Emma, that is when she gave up.
7) Okay, you know what? I am not going to argue this feat with you anymore. We are not going to see common ground with this. That said, maybe this feat is not as impressive as you make it out to be given Rachel's constant defeat at the hands of other psis. Maybe what the other psis can accomplish that Rachel can't is more impressive than this feat.
8) Actually, I dealt with it.