On the syntax of 'Cogitate quantis laboribus fundatum imperium (...) una nox paene delerit' (Cic. Cat. 4, 19)

Summary: the reason why this sentence seems unusual after translation is only because of the limits of English syntax, not because anything odd in the Latin.

A short form of expression combining two really distinct indirect questions

I do not understand why the commentator read the sentence that way. It is theoretically possible to read the first interrogative clause as subordinate to cogitate directly:

cogitate quantis laboribus fundatum imperium [sit]

Elliptic sit is not unreasonable in isolation, and fundatum imperium could be nominative. However, this is not possible with the other interrogative clauses, because it says quanta virtute stabilitam libertatem, not *quanta virtute stabilita libertas [sit]. The accusative makes that sit impossible, so libertatem and fortunas must be objects to something; and delerit is the only candidate:

Cogitate...quanta virtute stabilitam libertatem...una nox delerit

This makes perfect sense in Latin, but it cannot be translated literally, because this type of layered nesting is incompatible with English syntax ("think the-freedom-stabilised-by-how-much-virtue one night destroyed": this is ugly). The same applies to the third interrogative clause.

So, if we follow this commentator, we have three interrogative clauses with some ellipsis, supplied as follows:

cogitate quantis laboribus fundatum imperium [sit]
[cogitate] quanta virtute stabilitam libertatem [una nox paene delerit]
[cogitate] quanta deorum benignitate auctas exaggeratasque fortunas una nox paene delerit

But I think the lectio brevis makes much more sense—and is to be preferred stylistically—, i.e. a normal tricolon (three parallel constructions):

cogitate quantis laboribus fundatum imperium [una nox paene delerit]
[cogitate] quanta virtute stabilitam libertatem [una nox paene delerit]
[cogitate] quanta deorum benignitate auctas exaggeratasque fortunas una nox paene delerit

So I think this is the only reasonable reading of the sentence. It must be translated somewhat liberally, though; so I understand why those translations 'flattened' the syntax, turning it into four parallel interrogative clauses instead, adding the word how to introduce the final clause:

think with what great labour this our dominion was founded,
[think] by what virtue this our liberty was established,
[think] by what kind favour of the gods our fortunes were aggrandized and ennobled,
and [think] how nearly one night destroyed them all

The translation using which to introduce the fourth clause after flattening would seem an equally good option.

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In conclusion, there is nothing odd about the Latin; it is just English which is incapable of rendering the same construction.

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[Edit:] Let me illustrate the problem in English.

Think how much power one night destroyed.

This is possible. The interrogative phrase how much must come at the beginning of the interrogative clause: this is a strict requirement of English in the present context.

Think how strong an empire one night destroyed.

This is still possible, because how strong is at the beginning of the interrogative clause, and the adjectival phrase how strong can come before its head, the noun an empire. The latter is possible, because a plain adjective like strong can come before its noun.

Think how well established an empire one night destroyed.

The participial phrase how well established can again go before its head noun, so still no problem.

*Think by how much toil established an empire one night destroyed.

Suddenly, we lose grammaticality. The iron law of interrogative and relative pronouns requires that by how much should come at the beginning; however, the participial phrase is now such that it cannot be before the noun any more: *by how much toil established an empire is not proper English. The reason is probably that it becomes somewhat ambiguous or somewhat garden-path like: you could naïvely read established as a simple past now, a finite verb; or as a praeposited participial phrase modifying the verb ("by how much toil established did one night do something"); by the end, you'd know this was not right, and you'd arrive at the right reading: but that is too much work, it requires too much of the reader.

?An empire by so much toil established one night destroyed.

This is somewhat awkward, but perhaps still grammatical: with a moderate amount of puzzling or rereading, this sentence is readable. What I did was move the participial phrase to the right of its head noun. But I removed how. If we want to add how back in, we get this:

*Think an empire by how much toil established one night destroyed.

This is an alternative attempt at constructing the sentence: instead of moving the phrase by how toil established to an unnatural position to the left of its head, we keep it at the right. But now the problem is that by how much, the interrogative phrase, is no longer at the beginning of the interrogative clause. This is unacceptable in English, probably also because of a garden-path like issue: at a glance, you'd begin reading the sentence thinking an empire was some sort of object to think, which is wrong. That is why the interrogative phrase really must go at the beginning of an interrogative clause.

So we have two rules here which conflict:

• an interrogative phrase must come at the beginning of its interrogative clause

• a participial phrase of great complexity must come after its head noun