Yes to both. Ds8's now being homeschooled based on the issues you brought up with your questions and what we faced with the gifted schools and prior with special needs programs/schools. They had no clue with a 2e/pg child. Between the schools and various professionals, I can say that no one has ever seen a child like him before so he's often misunderstood and not accepted.
Ds8 was born with severe sensory processing. He had extreme sensitivity to everything (visual, auditory, tactile, taste, smell, vestibular, and on and on). It's improved over the years due to loads of therapies and interventions but at least less severe than it was. It still flares up when he's under stress, going through big developments, growth spurts, etc. I try very hard to minimize the stimulation with him and to keep ds on an even keel. Carol Kranowitz's book, The Out-of-Sync Child, is a classic on sensory processing
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http://out-of-sync-child.com/Those with PTSD (with or without extreme anxiety/perfectionism, etc.) can display these traits too. You can be hypervigilant with PTSD and this can heightened your sensitivities and awareness. Cognitive behavioral therapy and neurofeedback can help.
As to your question about coping with a 2e/pg child, that's a been journey to say the least. Andrew Solomon recently wrote a book, Far From the Tree, which included classical musical prodigies and children with a range of disorders/conditions (deaf, dwarfism, Down Syndrome, autism, transgender, born out of rape, etc.). Solomon also posed this question on how parents cope when their children are born so far from the norm and no where near what they expected/anticipated.
Solomon's book can help put things in perspective. Readers can perhaps discern how prodigies and 2e/pgness falls within the range of human experience. When I read the chapter on dwarfs and considered how so many of them face stiff stigma and have medical conditions that require extensive and very expensive surgeries, it helped me put our situation into perspective.