1) Try not to be too hokey, or simply recap your CV. In all honesty, I don't place much value in the personal statement
2) CV in its truest form is the most important part of the application. Publication record etc. is important, but expressing commitment to neurosurgery in particular is not a necessity. The CV helps to establish a track record of commitment to projects and success therein. It can be in GI or social sciences, but having experience developing an interest, researching, and publishing is important. That being said, if you initially started outside neurosurgery, having a transition towards neurosurgery is important. Likewise, a reason for this transition to discuss at the interview is important.
3) I'd rather not say for anonymity sake. It is a small field, you could easily find me knowing my position and alma mater.
4) This will be an issue. Even if you went to Oxford, not training in the US system creates a liability with respect to your medical knowledge base and clinical experience. Yes, doing well on Step-1 can offset the question mark regarding clinical knowledge. That being said, there are a multitude of IMGs who crush boards but just can not make the clinical connection on the wards. Likewise, clinical training abroad vastly differs from the US. Make sure you have a broad US clinical exposure, with letters, to verify you can successfully navigate the US medical environment.
5) So far as I'm concerned, Step-2 CK is the same as Step-3. Does not matter. That being said, if you bomb Step-1, take Step-2 early to show you can do well. Unfortunately, if you crush Step-1 and bomb Step-2, your advantage is lost.
6) The 4th letter would best be served as another academic US neurosurgeon. Make sure these neurosurgeons are either chairmen or titans (e.g. senior society members). There is no use getting a letter from someone who is an "academic neurosurgeon" who no one knows.
7) When asked during interviews, indicating your interest in pediatrics is acceptable. I would not recommend putting it in our personal statement. Much like medical school, residency is long and your mind on which sub-specialty to pursue (if any) changes