Learn English – Simple past or past perfect in this example

A bigger problem with all forms of 2 is that the second comma shouldn't be there.

In "However, they didn't know that Brian had flown to Brazil the week before, and had been abroad when the burglary took place." the comma breaks up the list of things "they" didn't know, which was one intended purpose of the "and". The "and" now makes the "had been abroad..." refer to the "they" instead of "Brian".

The "was abroad when the robbery took place" is a direct consequence of Brian's having gone to Brazil, and is the other purpose of the "and" (i.e. "and therefore").

A sentence shouldn't start with "however", either, so a better construction would be:

"They didn't know, however, that Brian had flown to Brazil the week before and had therefore been abroad when the robbery took place."

As an American English speaker, all four examples seem correct.

The past perfect often seems to be used in American English to avoid confusion about the relationship between two past events. Where such confusion is impossible, the simple past is often used.

"I had typed ten pages when he returned." indicates typing before returning. "I typed ten pages when he returned." implies that returning is simultaneous or even before the typing.

In your examples, "by the time" serves this temporal ordering purpose, so the choice of verb tense is unnecessary.