I can't think of an actual example where I would say "Why had you to ____"
In the question above I would have chosen 2 & 3, both are things I say regularly.
FYI I am also in the USA.
Syntactically, OP's first alternative (Could not you help him?) is more "correct", in that it places the negating not closer to could - the element it most applies to. But idiomatically today we almost always contract that to...
Couldn't you help him?
...even in "formal" contexts. But people often think of such contractions as "informal", and precisely because everyone normally makes the above contraction, the full form as given by OP tends to sound "strange" to the native ear. Thus, when looking for more formal phrasing we're likely to think in terms of discarding the contraction, but we avoid OP's #1 and go for #2 because it doesn't sound quite so odd.
In fact, given a formal setting (lawyer questioning witness, say) there's nothing at all unusual about...
"Is not this the murder weapon, Professor Plum?"
"Could not the gun cabinet have been left unlocked, Colonel Mustard?"
"Was not the dagger kept with the other cutlery in the kitchen, Mrs Peacock?"
OP's idea that the position of not determines whether it's a genuine enquiry or a complaint isn't quite right. What matters is that a complaint would stress the word not - which you can't do if it's contracted. You want that stress because effectively all the other words in the utterance apart from could and not simply describe the current situation (although less common, in most contexts it's possible to stress could instead of not when the intention is to complain about something rather than ask if it's true).
Note that it's not always possible to distinguish a question from a request. For example, given just...
"Could you not do that?"
...it can often be effectively impossible without further context to establish whether the speaker is asking you to stop doing something (complaint) or asking whether you're unable to do it (question).
In short, context and intonation are crucial in such negated constructions. Consider, for example,...
"Could you not do that?"
...which might mean...
1: You're doing it right now, and I want you to stop
2: It's what you plan to do, and I'm asking if you will (or are able to) change your plan
3: It's not what you plan to do, but I'm asking if you will change your plan
(and probably other possibilities)
If it's not obvious how #2 and #3 apply, consider "Could you not work tomorrow?", which could either be asking you to take an unscheduled day off, to work on a day when you normally wouldn't.
Best Answer
"Do you want to schedule a meeting?" is very straightforward. It is inquiring if the person wants to schedule a meeting.
"Did you want to schedule a meeting?" is more complicated and the meaning can change depending on the context as well as the inflection.
It could be inquiring if what you did was actually what you intended to do.
It could be asking what you want you want. Essentially synonymous with "do you"
It could also be discussing something you weren't able to do and inquiring if you had wanted to.