The phrase "who him" is also used in Jamaican dialect. It may mean "who is he?" , as well as "who does he think he is?." This depends on the situation in which the phrase is used and also the tone used to deliver the phrase. I tend to use it to mean "who does he think he is."
You're confusing traditional Latin grammar terminology with English grammar terminology,
and with modern linguistic terminology, as well.
Mood, Voice, and Tense were traditional inflectional categories of Latin verbs. I.e,
every verb in Latin was inflected (marked uniquely) for some mix of mood, voice, and tense.
Latin had six tenses (by a strange coincidence the same six you listed),
four moods (indicative, subjunctive, imperative, and interrogative),
and two voices (active and passive). That was Latin.
English has two tenses (Present and Past), no moods, and no voices.
In particular, English has no subjunctive mood, so you don't have to worry about it any more.
However, many other languages have rich inflectional systems, even richer than Latin.
Sanskrit and Greek both had a Middle Voice as well as Active and Passive, for instance,
and an Optative Mood (used for things one wishes and hopes for), and Sanskrit also had a Benedictive Mood (used for blessings).
And that's just Indo-European. There are lots of other ways to organize these matters.
Best Answer
This is just a tentative answer based mostly on my intuitions.
I think you have ordered the sentences according to decreasing likelihood that the condition is satisfied.
Though the difference between should and were to is certainly not very marked. I may have got this part totally wrong.
(Note: The variant of 1 in which the main clause appears to contradict the condition has more or less survived: all be it [that] is now spelled albeit. Also, be it that was often used in the following construction: be it that A, be it that B. It means something like: *maybe A, or maybe B. Though I think it can also mean: maybe because A, or maybe because B.)
As today, by choosing will/shall or would/should in the main clause, you could select how strongly to suggest that John won't ask.
Interpreting the choice between will and shall in the main clause is enormously complicated due to a series of mutually contradictory prescriptive rules fighting with each other and with the natural use coloured by the original meanings of these originally lexical verbs. See the Wikipedia article. Therefore I have so far ignored the fact that you used shall (not should) in 1 and would (not will) in 3.
Whether will or shall is used for pure, uncoloured futurity probably depends strongly on the author and genre in addition to the period. If both 1 and 3 are taken directly from the same source, then there may well be a meaningful difference, though it's not clear what it is. It would be most straightforward if dutifully could be added to 1 and/or readily to 3 without changing the sense much, but that's not the only option. It really depends on the author's personal style. According to one rule that is sometimes still seen, the meanings of will and shall are actually reversed for the first person.