Should he hear of the grim event that has just unfolded at the seafront—journalist Harry Jupiter being knocked off the pier dead* into the water—Brunswick will likely have a breakdown.

@avacadohats is correct, "dead" in this sentence is ambiguous.
Examples: "I hit the snooker ball dead into the pocket."
"His cat starred dead ahead out the window."

So it’s just as well that he knows nothing yet, otherwise that last fragment of hope which he still clings on to would probably be crushed.

You could also say "(...) which he still clings on" rather than "on to", both are perfectly fine options here.

Anyway, it has painfully dawned on Brunswick that last night he made some unwise and basic mistakes at the crime scene.

I really love this sentence! Very clever use of the phrase "it has dawned on" him, in contrast to the literal time period he is reflecting on, "last night".

I'd only suggest that you remove the conjunction in "unwise and basic" - you could just use a comma here instead, "unwise, basic mistakes".

In fact, overlooking a key piece of evidence - namely, a glass probably containing the fingertipprints of the culprit - is beyond doubt a negligent behaviour**.

Cool, and yeah you can also say "is beyond doubt being negligent", or I think this sounds even more natural, "is beyond doubt pure negligence".

He was so engroobsessed in pursuing his angle on Joanna Carver’s guilt, that he had become oblivious to anything that didn’t fit that view.

I would definitely add a comma after "guilt".

Reflecting now on that now, Brunswick feels regret.

Luckily for him, the forensic team did*** its job properly and did*** not fail tosuccessfully collected the glass as evidence.

Yes, your sentence was fine. Just offering an alternative :)

Should he hear of the grim event that has just unfolded at the seafront—journalist Harry Jupiter being stabbed to death and knocked off the pier dead* into the water—Brunswick will likely have a breakdown.

In response to your question, this does not make it clear that Harry Jupiter died as a result of being knocked off the pier. You would need to add some detail to this, such as he was killed before entering the water (e.g. he was stabbed with a knife) or he drowned as a result of entering the water.

Anyway, it has painly dawned on BrunswickBrunswick had come to the painful realisation that last night he made some unwise and basic mistakes at the crime scene.

In fact, overlooking a glass probably containingthat almost certainly had fingertipprints of the culprit on it is beyond doubt a negligent behaviour**.

You can use beyond doubt in the way that you have here.

He was so engrossed in pursuing his anglehad been so fixated on Joanna Carver’s being guilty that he had become oblivious to anything that didn’t fit that view.

Reflecting now on that now, Brunswick feels regret.

Luckily for him, the forensic team did*** its job properly and did*** not fail to collect the glass as evidence.

This is correct - you would say 'and did not fail to collect the glass as evidence'.