Could one of Voldemort's Death Eaters have killed or harmed Harry at Privet Drive?

Question

In Order of the Phoenix, Dumbledore explains to Harry the protection that the Dursleys' home provides:

While you can still call home the place where your mother's blood dwells, there you cannot be touched or harmed by Voldemort. He shed her blood, but it lives on in you and her sister. Her blood became your refuge. You need return there only once a year, but as long as you can still call it home, there he cannot hurt you. Your aunt knows this. I explained what I had done in the letter I left, with you, on her doorstep. She knows that allowing you houseroom may well have kept you alive for the past fifteen years.

Dumbledore says that he cannot be "touched or harmed by Voldemort". Does this mean that he could have sent a Death Eater to just bust down the door and kill Harry, assuming that Voldemort would allow them to? And even if he didn't want them to kill him, could they have harmed him in some other way (e.g. the Cruciatus Curse)?

Answer 1

No. Harry was protected from Death Eaters and Voldemort's allies, not just Voldemort himself.

Dumbledore explicitly states that when devising Harry's protection at Privet Drive that he was intending to protect Harry from the Death Eaters as well as from the Dark Lord himself.

"My answer is that my priority was to keep you alive. You were in more danger than perhaps anyone but I realised. Voldemort had been vanquished hours before, but his supporters - and many of them are almost as terrible as he - were still at large, angry, desperate and violent."
_{(Order of the Phoenix, Chapter 37, The Lost Prophecy).}

Dumbledore therefore wanted to protect Harry from Voldemort when he managed to regain a body at some point in the distant future. But he also wanted to protect Harry in the short-term from the wrath of Voldemort's supporters. He subsequently cast a protective charm that would defend Harry from any who would wish him harm.

We do additionally have some insight into the perceived impregnability of Privet Drive from key figures from within the Death Eaters. Snape describes it as a "place of safety".

"My Lord, the Order of the Phoenix intends to move Harry Potter from his current place of safety on Saturday next, at nightfall."
_{(Deathly Hallows, Chapter 1, The Dark Lord Ascending)}

And Voldemort says "not even I can touch him" at Privet Drive.

“But how to get at Harry Potter? For he has been better protected than I think even he knows, protected in ways devised by Dumbledore long ago, when it fell to him to arrange the boy’s future. Dumbledore invoked an ancient magic, to ensure the boy’s protection as long as he is in his relations’ care. Not even I can touch him there..."
_{(Goblet of Fire, Chapter 33, The Death Eaters)}

Presumably, that means 'everyone up to and including me'. Essentially, it would be a huge security loophole to only protect Harry from one person and one person only (even if that person was Voldemort). I'm sure that Dumbledore's charm covers any and all individuals who may wish to cause Harry harm. One way of keeping Death Eaters out would be to prevent anyone with a Dark Mark from entering the area.

Even if Death Eaters were somehow able to enter Privet Drive under Dumbledore's protective charm I think the above quotes show that Voldemort believes that Privet Drive is a no-go zone for his forces. Perceived security coverage can be just as effective as actual security coverage. Voldemort believes that no Death Eater can enter Privet Drive. And, as RichS says, he had a specific obsession with personally killing Harry himself; he wouldn't have entrusted that task to one of his minions.

Answer 2

No

I believe it was mentioned in 5th or 6th book even with Death Eaters, but I'm not completely sure where, so until a quote is found, I have only this wiki:

Albus Dumbledore first visited the house in 1981, delivering the baby Harry Potter to be put into the Dursleys care after the murder of his parents. Harry wasn't the only thing that Dumbledore left behind him on this occasion: he also invoked strong magic granting Harry absolute protection from Lord Voldemort and his Death Eaters whilst he was at the house, as long as Harry could still call Privet Drive his home, until he came of age on his seventeenth birthday.

spoiler:

Well, at least for the time Dumbledore was alive

Answer 3

The Dark Lord didn’t think so, at least.

When the Dark Lord made his plan to kidnap Harry from Hogwarts, he chose his plan to use the Triwizard Tournament considering that Harry would be too well protected at the Dursleys’ from any method of retrieving him.

“For he has been better protected than I think even he knows, protected in ways devised by Dumbledore long ago, when it fell to him to arrange the boy’s future. Dumbledore invoked an ancient magic, to ensure the boy’s protection as long as he is in his relations’ care.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)}}

Presumably he thought this protection extended to the Death Eaters as well, since he had no problem having a Death Eater kidnap Harry from Hogwarts - that was his final plan.

“Use my one faithful Death Eater, stationed at Hogwarts, to ensure that the boy’s name was entered into the Goblet of Fire. Use my Death Eater to ensure that the boy won the Tournament – that he touched the Triwizard Cup first – the Cup which my Death Eater had turned into a Portkey, which would bring him here, beyond the reach of Dumbledore’s help and protection, and into my waiting arms.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)}}

The Dark Lord didn’t insist on retrieving Harry himself. He relied on Barty Crouch Jr. to get Harry out of Hogwarts and to him.

“He told me he needed to place a faithful servant at Hogwarts. A servant who would guide Harry Potter through the Triwizard Tournament without appearing to do so. A servant who would watch over Harry Potter. Ensure he reached the Triwizard Cup. Turn the Cup into a Portkey, which would take the first person to touch it to my master.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 35 (Veritaserum)}}

Presumably, then, he’d have no problem having Barty Crouch Jr. get Harry from the Dursleys instead. Therefore, it’s likely that the reason he didn’t try that is because he thought the protection Dumbledore used would also work on Death Eaters, and make it impossible for them to get at him there.