or should I not do young scholars in favour of doing more AP exams?

If you’re taking a rigorous course load and several NZQA scholarship subjects, you really won’t need APs - especially considering that young scholars program.
Are you doing NCEA, CIE or IB?

If you’re a CIE/IB/NCEA student, the only reason you should be doing APs are

1. your CIE/IB/NCEA grades are not good and you want to prove your academic potential through extra exams
2. you want to take rare AP subjects to show your breadth to universities such as Computer Science

Otherwise, if you already have a rigorous course load of university courses and scholarships, APs are a waste of time and find a better investment of your time.

I’m doing NCEA

If your grades are good, and you’re doing scholarships, I wouldn’t worry at all about doing AP subjects. No one I know who’s gotten into Ivies/MIT/Stanford among my peers did them. Focus on excelling at your local curriculum!

My NCEA AME ratio is approx 16:30:82 at Level 2 and is not too different at Level 1. Am I correct in my understanding that these are poor results for schools with acceptance rates at or below 10%? And if so, are my grades beyond saving? I assume my class rank is hovering at around the top 15%.

Your results roughly translate to a 3.5 GPA, which is pretty good, but not great for top universities with acceptance rates below 10%. Those universities are looking at GPAs above 3.6.

If you take some Scholarship exams and do well in those, you can show the universities that you are academically capable. High GPA is great, but rigor of courseload matters more.

What is rigorous? 5 NCEA and 5 NZQA scholarship subjects?

It really depends on which school you are targeting. 5 NCEA and 5 Scholarships seem like the norm for most top candidates. I would say 8-10 NCEA Level 3 + 8-10 Scholarship exams is the upper bound and 5 and 5 would be the bare minimum.

That’s the max offered at my school, so I couldn’t take anymore, could possibly do 6 NZQA scholarships - does this still provide me good chance for competitive schools such Harvard, Stanford, MIT and getting 1500+ on SAT? and 700+ on subjects?

Again there is no right answer to your question as it depends on a variety
of factors.

Normally for those schools you are looking at 1550+ in sat and 750+ in
subject tests.

For nzqa scholarships you are looking at becoming at least an outstanding
scholar.