Learn English – If you want to wake up at 7 tomorrow

There are two aspects of correctness in those sentences.

First, and we can dispense with it right away, some verbs use the wrong person, wrong form, some nouns are missing necessary articles or pronouns. Example: When the sun sets, the farmer desides to eat his food. But that aspect is not what you were asking, is it?

Second, and this is the real subject of your inquiry, I think, pretty much all of those sentences use the correct tenses and moods for subordinate and main clauses.

If you work hard, you will pass the examination.

becomes (in subjunctive mood)

If you worked hard, you would pass the examination.

So, to answer the main question, yes, most are OK. I'd watch out for proper verb forms:

If you sung sang the song, you would practice efficiently.
If you had sung the song, you would have practiced efficiently.

The only general rule for conditionals is that the condition and consequence clauses must have the same degree of "reality", which may be expressed in the verbform or with a modal verb.^† Note, however, that the degree of "reality" expressed by a particular verbform or modal is a function of context, not the verb itself; it would perhaps be more accurate to speak of the verb "agreeing" with the reality rather than "expressing" it.

• The first sentence is an inference conditional: If P, then Q = "If fact P is true we may infer that fact Q is true". There is no constraint on the temporal location of the facts; we may infer a non-past fact from a past fact, as here, or a past fact from a non-past fact, or any other combination.

• The second sentence is an actualization conditional: If P, then Q = "If eventuality P occurs then eventuality Q follows". The temporal location of eventuality P must be prior to that of eventuality Q. In this case, the unreal past eventualities they had found the killers and there had been a proper investigation are followed by a hypothetical/unreal present consequence: we would not have to see the eventualities which we do see right now.

The sentences are fine; the problem is with your "rules".

What I call the "n-conditionals"—zero, first, second, third, conditional—are not employed in linguistic descriptions of English.^‡ They are pedagogic devices for introducing students to the structure of conditional expressions. They describe the most common uses of four common syntactic forms, but they are very far from exhausting either the catalog of acceptable syntactical forms or the semantic uses of the forms they describe. By way of example: I once tried to count the distinct sorts of conditionals described in Declerck & Reed, Conditionals: A Comprehensive Empirical Analysis, de Gruyter 2001; my count broke down somewhere around 130!

The n-conditionals are baby rules. Your understanding of English has evolved past their very limited utility, and they are now obstacles to your understanding. Discard them.

^† _{But in casual speech this "rule" is often abrogated, particularly with complex hypotheticals.}

^‡ _{The terms seem to have been borrowed in the 1960s from terms sometimes employed in the description of inflectional forms—not syntactic forms—in other European languages; I've been unable to pinpoint exactly when they entered English pedagogy.}