English tense usage can't be divided into fact and non-fact:
If + should can be used in type 1 to indicate that the action, though possible, is not very likely:
If + would like/care can be used instead of if + want/wish and is less polite:
If you will/would is often used in polite requests and would is the more polite form:
If you would + infinitive is often used alone when the request is one which would normally be made in the circumstances:
In colloquial English or (+ else) can often replace otherwise:
It's time can be followed by an infinitive:
Suppose can also introduce suggestions:
There are certain constructions (including conditional sentences) that have a hypothetical meaning, and the unreality that they express is shown by shifting the verb form "backwards":
There is a Past Subjunctive in English, but it is only visible with the form were to express non-fact:
We do not always have to stick rigidly to the three types of conditional sentences. There are occasions when we can use any tenses in if-clauses, depending on the context:
We form Type 3 conditionals with if + Past Perfect (or if + could have) + would have:
Would rather + the Past Perfect is possible, but it is more usual to express the same idea using wish:
Рrovided (that) can replace if when there is a strong idea of limitation or restriction. It is chiefly used with permission: