These "imaginary scenes" sound like blurbs publishers post inside dust jackets on books and elsewhere. Example 1 is fine except for this one sentence:
Two days ago, they once met at a library.
I think you mean: They met once at a library.
"They once met..." gives the impression that at some point in the past they met. "They met once..." gives the ...
It is not a case of as you have called them imaginary situations, if we take your examples into consideration. Such case is embraced in such section of the grammar as stories, commentaries and instructions.
Present tenses are often used informally to tell stories. The simple present is used for the events – the things that happen one after another. The ...
The first two examples sound like they come from the eighteenth century. Where were you taught this, and with what materials?
Using the present subjunctive with such verbs is rather archaic these days, or at least affected. The usual marker for the subjunctive here is "that," although it may be omitted ("suppose that..."; "assume that...").
You do still ...
"As it were" is used for making a description sound less definite and less exact. Collins dictionary defines :
"As it were" means "as if it were really so".
Therefore, both your sentences are ok and denote the same meaning.
The negative subjunctive is formed by putting not before the verb, at least nowadays, as indicated in e.g. this Q&A on our sister site English Language & Usage: What's the correct form of the negative subjunctive?. (That seems to imply it used to be the other way around.)
That means the sentence should be
The Senate has decided that such students ...