explain the difference between the alternative expressions and give
the context in which one should be preferred to the other(s).
This is the main part of the question, so ...
"this question should not be closed" doesn't get at the fact that the
closing already occurred.
Right. Let's break it down. "should not be" differs from "will not be" (or "is not to be") in that it introduces ambiguity. Arguably it is a subjunctive example, i.e., (I would argue) the "should" suggests something that is dependent upon something or that is contrary to actual fact. In order to suggest an action has already occurred, you need the tense to change, so
should not have been closed
does this. (Take out the "should" and you must change the construction to "was not closed", which is past tense & unambiguous.)
was not to be closed
Is wonderful, but awkward. By this I mean it illustrates some linguistic mental temporal acrobatics, but is lacking. It suggests that something may not have or may have occurred in the past, but that there was something (or someone), a rule perhaps, or force, or a person, acting upon someone's choice or ability to change the situation. It is awkward (lacking) because it doesn't do the job of telling us what actually took place (in a funny way, it is almost the same as its opposite, "was to be closed", because we just don't know for sure whether it was closed or not). "was not to be" and "was to be" each suggests that the opposite may have occurred -- each suggests a "but" is coming: "it was not to be closed, but Edward was determined to close it"; "it was to be closed, but Edward found a way to keep it open". It reminds me of the expression "I was not to be outdone", which suggests I may have ultimately gotten the upper hand, but not necessarily! Consider also that "the question was not to have been closed" gives us the connotation of the question having been closed at some point, but it is very ambiguous.
or are there better ways to express the idea, i.e., 'it should not
have been closed'?
That's it. It is clear that it was closed, but that the closing was not desired (by someone, probably you), or that there was a rule that was broken.
(Since you are concerned with correctness, I'll throw in that "i.e." [id est] is not what you want here, but "e.g." [exempli gratia], because you are giving an example instead of giving an alternate expression. Extra credit.)