Well, the terminology "locally" and "globally" kind of confuses me
. Referencing your original post, an HH guitar essentially has 4 coils. The bridge has coils 1 and 2, the neck has 3 and 4. With a typical 3-way toggle switch, including those used by Ibanez, the middle position has 1+2 in series, 3+4 in series and the combination of the two set of coils in parallel with each other.
In the switches diagram as you see. When pickups are connected in parallel, they colourize it in yellow not it that reddish colour.
I don't see anything on that page that indicates what the reddish color is supposed to represent. Just because they use red to indicate series connections on some other wiring diagram doesn't mean anything in this picture. Besides which, this isn't a technical diagram, it's just marketing material. The color merely indicates which pickup is active in each switch position.
Does the 3 way toggle differs from the 3 way switch if we are using 2 HBs only ?
I don't quite understand the question. There are different kinds of 3 way toggles used for different purposes, for example, DiMarzio makes one, I believe it's the DP1111, that can be used to get John Petrucci's wiring on an HH guitar (full bridge - inner coils - full neck).
What i understand that the pickups are connected in parallel with each other whatever combination it is, but the coils of a humbucker could be either connected in parallel or series with respective to each other, Am I right ?
Absolutely. You could easily wire a 4-conductor humbucker such that the coils are permanently in parallel with each other, if that's the sound you wanted. Or you can add an extra switch to give you both options, which is more typical.