It is not a requirement. The requirement is 2 years of world history and 1 year of US.
Part of the issue is that public schools and many private schools allow kids to double up on core classes because they can take 7 classes a semester. The 5 classes limit is what is hard.
I’m not a professional admissions person (unlike some here) but I think it would be fine to take only 3 years of language since he is already at an advanced level. As @Mwfan1921 mentioned, many if not most colleges will look at the level he has achieved in Spanish (5 or 6) and consider this sufficient.
I think advanced physics and chem would be really useful for an engineer. If he takes only one of those, I would prioritize physics. I also think it’s important to have a math class senior year, and I think social science in senior year is more important than another year of language.
Totally understand. Our HS has only 6 periods and lots of requirements, so it can be difficult to fit in electives.
The class he is taking now, which is like a souped up proof based calc class is considered the hardest class at the school. He is the only sophomore in the class so the path after is a little unclear. The Linear Algebra (equations was a typo) can be a semester or a year. If you take the year they add other content. But it only has a calculus co-req, not a pre-req, and most kids who take it take it with the “regular” calc sequence which is closer to AB and BC. But he has to take that class because they require 3 years and Stats (which I understand to be similar to AP Stats) is for seniors only.
The independent study is what they have said he could do, but it’s not a common thing, so I don’t know what they would teach.
I think an online class would be hard, unless someone has one to suggest.
The question I have is which of these sequences look best
Take AP stats exam in 10th get a 5, take Stats in 12th, with calc based physics
WDon’t take or report stats exam, take Stats in 12th, with calc based physics
Take AP Stats exam in 10th, get 5, take Calc based physics and post AP in Chem
Take AP Stats in 10th, get 5, take Calc based physics and independent study math in 12th.
Is the school’s stats class calculus based (like a college stats class)?
Just a crazy thought - just thinking out loud - and not saying it’s a good thought - but knowing a Calc BC kid Senior year is extremely advanced and your student is there Sophomore year and I think you said earlier, he couldn’t get to a college to take a higher level class and I agree online classes are tough - is this the right school? Is there another that might be able to offer him more?
Again, crazy thought - but just putting it out there - don’t know the answer - but two years of not having a realistic math to take - might that undermine him later?
No, it is very close to the AP Stats curriculum. It does not have a calc prereq and the school doesn’t count it towards the 3 math classes required for graduation.
I think the Linear Algebra is fine for him. It will be likely easier for him than the course this year but the content will be new.
I am less convinced that taking stats when he will already know the content makes sense. I feel like calc based physics and advanced chem would keep his math skills up. But I worry about not having 4 years on the transcript.
I think it’s a good fit for him. He had some choices and there were a lot of reasons we thought this was a good fit that still stand.
If the stats class is just like AP Stats, then independent study math is probably the way to go. I do think it’s important to have some kind of math on the transcript in senior year.
I personally don’t think it would matter much one way or the other to have a score on the AP Stats exam without taking a class. AP Stats is also not that useful because it doesn’t replace college stats (unlike AP Calc). Of course if it’s no trouble for him, he could take the exam if he wants. 
I think he’s good for EC’s. He is very involved in tech theater and robotics, plays several varsity sports and does a bunch of things, including a lot of service outside of school.
Taking a self study AP test and then taking the class later is usually not looked upon favorably by admissions officers. Looks like grade grubbing. I wouldn’t advise this option.
Maybe/probably, but he still needs 4 years of math in HS. So then independent study it is (I would first find out what that content would be), or any of the many online providers where he could take Calc 3/multivariable. Look first at in-state school options, incl CCs. But there are dozens of reputable online providers of Calc 3, including many colleges. Talk to his counselor too of course.
Are there online providers that are reputable and 100% asynchronous? I would love a recommendation if one exists.
Also if he uses an online provider and his HS doesn’t accept the credit, can it still count as the 4th year? Does he have to take it during his senior year or could he take it this summer or during junior year?
Being already at AP 5 level in Spanish, it may not matter too much for college admission purposes to go higher, compared to getting to AP level in Mandarin as well. Indeed, if he has outside ways to improve Spanish, then he may derive more learning value from improving Mandarin in school.
Is there anything that he feels he just wants to take, separate from what will look good on an application?
Tech Theater, Mandarin, as much science as possible but particularly the calc based Physics.
That’s what he was hoping but it sounds like people are saying it doesn’t work like that.
I think if you have enough in one language, then doing another language is not gong to hurt and likely will help. They want one language - if you deliver two to the level they want in each….
At some point, the kid is such a stud, becoming stud-lier may not matter. And it depends on the school too….
Kids aren’t expected to be in the stratosphere - and yours is - squared.
So I think you have little to worry about.
sounds like you have your answer, when kids are so advanced does it really matter the specifics beyond what they want?