This is another subjunctive and conditional question. I am interested in the formal, even archaic, uses, not just the modern uses (I am given to understand that the subjunctive is disappearing from use, for the most part). I am interested to know if my examples are accurate, if there is anything important I have missed, and finally there is a specific question on the use of the subjunctive in mixed conditionals. If you feel there is anything important that needs to be borne in mind concerning subjunctives, please include it.
According to The University of Ottawa Writing centre (here), the subjunctive is used:
"...in dependent clauses to express unreal conditions..."
My attempt: If I were a skilled footballer, I should be rich.
"...in dependent clauses following verbs of wishing or requesting."
My attempt: I wish I were a skilled footballer.
My attempt: I insisted he call her today.
Strangely enough, It doesn't seem to be used with "hope".
The subjunctive mood is used in a dependent clause attached to an independent clause that uses a verb such as "ask," "command," "demand," "insist," "order," "recommend," "require," "suggest," or "wish."
My attempt: The king ordered the soldier be shackled, before he escape. (Setting aside the issue of whom the pronoun "he" belongs to, is "escape", as oppose to "escapes", correct?)
The subjunctive mood is also used in a dependent clause attached to an independent clause that uses an adjective that expresses urgency (such as "crucial," "essential," "important," "imperative," "necessary," or "urgent").
My attempt: Melinda said that it is necessary that she skip through the park; it makes her feel better.
On the wiki page for conditionals (here), if identifies zero, first, second, third and mixed (second and third) conditionals.
The zero conditional can make use of the subjunctive, according to wikipedia, but this is archaic:
"If the prisoner be held for more than five days, ..."
My attempt: When/If there be light rain, the ground will be moist.
The subjunctive is used in second conditionals, and I believe this is the same as the first example (expressing unreal conditions).
"If I (he, she, it)... were rich, there would be plenty of money available for this project."
The third conditional is used "to refer to hypothetical situations in a past time frame, generally counterfactual... Here the condition clause is in the past perfect, and the consequence is expressed using the conditional perfect." So, despite being counterfactual, or percieved to be counterfactual, there is no subjunctive (perhaps it is equivalent in form and therefore is ignored/"doesn't exist".
"If you had called me, I would have come."
Having established this, I am confused by the mixed conditional.
""Mixed conditional" usually refers to a mixture of the second and third conditionals (the counterfactual patterns). Here either the condition or the consequence, but not both, has a past time reference... When the consequence refers to the past, but the condition is not expressed as being limited to the past, the condition clause is expressed as in the second conditional (past, but not past perfect), while the main clause is in the conditional perfect as in the third conditional: If we were soldiers, we wouldn't have done it like that." (emphasis mine)
Since the "condition clause" is from the second conditional, why does it not feature the subjunctive? My attempt: If I were a soldier, I wouldn't have done it like that.
I would like to thank everyone for their contributions; I am expanding the post due to feedback as there is clearly more to consider regarding the subjunctive.
I am unclear as to the differences between the irrealis and the subjunctive. It has been pointed out that they are related; I get the impression that the irrealis is just the exception to the rule for how to form the subjunctive in the past:
The present subjunctive, both are the bare infinitive:
To learn: I insisted that he learn to appreciate hats.
To be: I insisted that he be a hat connoisseur.
The past subjunctive is the exception: all taking the simple past, except to be:
To smell: I insisted that he smelt hats.
To be: I wish that he were a hat-smeller.
To me, it doesn't seem to have a different role.
Another issue is the future subjunctive. Here, again, "were" pops-up:
To manufacture: If I were to manufacture hats, I would never have to buy one again.
To be: If I were to be a hat manufacturer, I would never have to buy a hat again.
Were makes some (seemingly) random appearances...
As for the archaic references, I wasn't too specific, my apologies. I suppose I meant more Georgian/Victorian/Edwardian eras than Shakespeare.