In answer to your specific questions:
1. The VECI may be valuable if you are interested in using it to obtain access to resources such as DYS, since a VECI in the same range as your DC's VCI would be in the qualifying range, but a single primary index score (i.e., the VCI) would not meet criteria. This requires two additional WISC-V subtests, preferably given by the same examiner. Otherwise, I would not normally pursue the VECI.
2. The large diversity of cognitive scores is not necessarily concerning in itself, but does give one pause in combination with the diverse achievement scores, and with your reports of academic frustration, anxiety, and emotional dysregulation. Posters above are accurate in noting the parallels between cognitive strengths and academic strengths, and the importance of trusting your holistic understanding of your child.
3. There are different definitions of intellectual giftedness out there, even among professionals, but I think most clinicians would consider GT-level scores of this magnitude to constitute giftedness, even if they occurred in only one index.
If one were to pursue further testing, either through the school or privately, one might want to include
a) comprehensive academic achievement (even in the strength areas, as there may be subtleties), rather than a computerized multiple-choice test (which is what you have now) (typically by a psychologist or educational diagnostician)
b) assessments of social language (pragmatics) (speech language pathologist)
c) social-emotional assessment (psychologist)
d) measures of fluency/retrieval efficiency/memory & recall (psychologist)
e) fine-motor skills assessment (occupational therapist).
