I can't figure out which one is the correct formal one or if all the variations can be used:
Is there a context in which they would be different/incorrect?
I could not find an answer for this among the already asked questions but if this is a duplicate please feel free to mark it as such.
"Shouldn't it be" is correct but informal. This is shortened from the formal "Should it not be" which is also correct.
"Should it be not" is not correct in this context.
A point to notice is that "Shouldn't it be this?" and "Should it be this?" have very similar meanings, despite one of them having a "not":
"Should it be this?" Is asking if the thing the speaker refers to is correct.
"Shouldn't it be this?" Is asking if the thing the speaker refers to is correct and shows that they think the current solution is wrong.
"Shouldn't it be" is correct for all situations other than extremely formal writing. It would be used to start a question -- "Shouldn't it be blue rather than orange?"
"Should not it be" is also correct, but sounds really awkward and old fashioned. You would more likely use "If it were not blue but orange, "
"Should it not be" means the same thing. It forms a start to a hypothetical with the same meaning as "If it were not blue, I would not like it."
"Should it be not" is also very archaic sounding but correct. The meaning is a little different, though. It also forms the start to a hypothetical like "Should it be not blue but orange, I would not like it" That's very awkward sounding too. You would more likely use "If it were blue rather than orange..."
