Grammar - the suppositional mood

I've started to learn grammar online (http://uastudent.com/category/english/english-grammar/) and here is what I've learned so far about suppositional mood.

Analytical form, built up with the help of the auxiliary verb "should" for all persons + infinitive. Expresses problematic actions (desirable, suggested, required…), which are not necessarily contradict reality. Expresses the same modality as Subjunctive I, that's why they can be used in the same syntactic structure. They are quite interchangeable and differ mainly stylistically.
In simple sentences. Used only in interrogative sentences beginning with "What if…" (And what if he should come back?).

In complex sentences. In Nominal Clauses it is used in Subject Clauses beginning with the introductory "It" in the principal clause when the modal meaning is expressed (It's important that he should come on time), after the expression of emotion (It shocked me that he should have been so cruel) and after the expression of fear (I feared lest he should find it out). In Object Clause it expresses the meaning of recommendation, suggestion, advice, insistence, etc. (He ordered that we should come). It may be used in Attributive and Predicative clauses. In Appositive clauses it usually modifies abstract nouns (idea, feeling…) and introduced by conjunctions "that, whether, as if, as though" or adverbs "how, why". The parts are not separated by comma (Her feeling that something else should happen surprised me; There's no reason why you shouldn't read it).

In Adverbial Clauses of purpose the Suppositional Mood is introduced by the conjunctions "so that, in case, lest" (He whispered these words lest somebody should overhear him). In Adverbial Clauses of concession it is introduced by the conjunctions "though, although, whatever, however, etc." (Though he should make every effort, he can't make it to the top). In Adverbial Clauses of condition referring to the future it's used to show that the action is possible though unlikely. In the principle clause the Imperative, Conditional or Future Indicative is used (Should he drop in tell him to wait for me; If I should meet her, I should tell her all about it; Should it be snowing we will stay in).

The conditional mood

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In simple sentences. The Conditional Mood can be used in simple sentences beginning with "But for…" (But for the rain we should continue our way). It's also used in sentences with implied condition (I wouldn't waste my time on such things in your place). The mood is used by the speaker so as to sound polite (less straightforward) (I should like to speak to her).

In complex sentences. Real conditions.
Zero condition (General truth) – used with conjunctions "when, if, unless, provided". One action or result always follows another one (Oil floods if you pour it into water).
Type I – refers to the future (I will help you if you need my help; If I fall in love I will get married).
Unreal conditions.
Type II – the verbs in the oblique moods directly refer to the present or the future (If I could play the guitar, I would be in a rock band).
Type III – the action or the result refer to the past (If I had known of your arrival yesterday I should have met you).

Mixed (split) conditions – a) the present unreal condition and the past unreal result (If I were rich, I would have bought a big house a long time ago); b) the unreal condition refers to the past and the unreal action refers to the present (If he hadn't wasted so much time, he wouldn't be so nervous now).