Learn English – “If only + would have/could have” conditionals

The following sentence does not use "if only..." idiomatically, IMO.

If only he would sell me his car this week, I would give him $1000 more.

In an if-only statement, the independent (main) clause expresses something that becomes possible when the if-only condition is true. The thing made possible is something that is wished for.

In your example, "I would give him $1000 more" is not something that is made possible and wished for. It is a quid-pro-quo.

If he would sell me his car this week, I would give him $1000 more.

But this following sentence would be idiomatic if his selling you the car would allow you to drive to a gig where you could earn the additional money, for example; if you had a fleeting opportunity:

If only he would sell me his car this week, I could give him $1000 more.

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.}