Welcome to the forum cc6 - you'll find good advice here. I can't help with the autism questions as my 2e kiddos have other types of challenges, but fwiw, if you are looking for further (private) testing, some of us here have been able to have neuropsych evaluations covered by our medical insurance - in our ds and dd's case, both were dealing with anxiety and the neuropsych was recommended by our ped to determine if there were causes for the anxiety (and there were, related to disabilities that impacted their ability to function at school). I also wonder if your ds has been evaluated by a developmental pediatrician at some point? That also would most likely be covered by medical insurance, and my understanding (from our ped) is that is the route that most families pursue here when there is a question of a potential autism diagnosis.
Even though they are potentially very expensive, I've found in our own family's journey, that having the private evaluations was extremely helpful in understanding our children's needs.
Re is your child gifted or not, I've found testing to be helpful in providing data that helps me understand my childrens' areas of challenge as well as areas of strength, and as they've gotten older it's been really important to be able to help focus on areas of strength in addition to accommodating and remediating and dealing with coping with challenges. OTOH, I've probably learned more about their strengths simply by getting to know them well, by being closely involved in their schoolwork, by watching closely as they navigate homework, group play, life in general etc than I have learned through testing - so if you can't get further testing for awhile, and if you don't need it right away for advocating or getting into a specific program, I wouldn't worry about testing and instead just spend time working with your child
Best wishes,
polarbear
ps - forgot to add - doing what you're doing here - asking for advice from other parents, has also been *extremely* helpful to me over the years
