Was the Fidelius Charm responsible for hiding Grimmauld Place from both Harry and the local muggles?

Question

I've recently discovered that Chapter 12 of Deathly Hallows tells us that Grimmauld Place has been hidden to muggle eyes for a long time:

The Muggles who lived in Grimmauld Place had long since accepted the amusing mistake in the numbering that had caused number eleven to sit beside number thirteen.

This suggests that the building has been hidden for longer than The Order has used it for. This means that it must have been hidden prior to Dumbledore's Fidelius Charm on it.

However, chapters 3 and 4 of Order of the Phoenix seem to very strongly imply that the house became visible to Harry only when he had learned the secret that was the target of the Fidelius Charm:

Harry looked down at the piece of paper. The narrow handwriting was vaguely familiar. It said:
The headquarters of the Order of the Phoenix may be found at number twelve, Grimmauld Place, London.
[...] Harry looked around at the houses again. They were standing outside number eleven; he looked to the left and saw number ten; to the right, however, was number thirteen.
"But where’s — ?"
"Think about what you’ve just memorized," said Lupin quietly.
Harry thought, and no sooner had he reached the part about number twelve, Grimmauld Place, than a battered door emerged out of nowhere between numbers eleven and thirteen

So what is actually responsible for hiding the house? Deathly Hallows seems to say that it can't be Fidelius, but Order of the Phoenix strongly implies that it must be.

The natural guess is that there are two layers of protection - whatever existed previously and then the Fidelius Charm - but, if that is the case, then why does Harry knowing the secret - something that doesn't actually mention the existence of the house - defeat all of these protections? Are we to believe that the only other relevant protections on the house are strictly anti-muggle? If so, then how can we explain The Order being concerned about Bellatrix being able to find the house in Half-Blood Prince, where the Fidelius Charm (which, by assumption, is the only relevant charm protecting the house) should have protected it fully?

Answer 1

Grimmauld, 12 was used for ages by Black family as a residence.

The charm hiding the house from Muggles was not Fidelius, but some other (unspecified) Muggle repelling charm commonly used by Wizarding folk to hide their dwellings.

Although it is not explicitly explained in the books, the current Magical law (The Secrecy Act) required any Magical family to use all necessary precautions to prevent Muggles from seeing them doing magic. The best way to do it in a big city would be to make the house totally inaccessible to Muggles. Same way as The Ministry of Magic, Hogwarts, Gringotts and other major Magical buildings in London. As it is explained with Hogwarts, the charms (unspecified) make the place invisible and unplottable, i.e. it is magically hidden from any maps or navigation equipment muggles use.

So, Muggles do not see the house at all, they see houses 11 and 13 adjacent to each other, with no gap.

A similar enchantment is described in Deathly Secrets, where Muggles see some war memorial instead of a monument to James and Lily Potter.

After the house became The Order HQ, however, Fidelius Charm made the house invisible to Wizards/Witches as well, unless they were given access by the Secret Keeper.

The Order's concern about Bellatrix was due to the fact that she might challenge Sirius's (and later, Harry's) inheritance of the house, and enter it as a rightful owner. There is some hole in this protection scheme connected with wizarding inheritance laws conflicting with magical loyalty, and it is due to the fact that the house had many layers of enchantments placed upon by generations of Blacks, and has its own sense of loyalty. You may compare it to Kreacher, who is extremely loyal to the family, but has to obey Harry as his rightful master.

Harry fits all the requirements to gain access to the house. In the events of Order of the Phoenix, he is recognized by the Fidelius Charm, and other protection recognizes him as a guest of the house owner - Sirius Black, who is a rightful heir to the House Of Black. Later, with Sirius's demise, the ownership transfers to Harry by Sirius's will. So again, he fits all the requirements as the rightful owner and the Order member.

Answer 2

No, the Fidelius Charm only comes on top of it

This is what Sirius has to say about Grimmauld Place:

"It's ideal for Headquarters, of course," Sirius said. "My father put every security measure known to wizardkind on it when he lived here. It's unplottable, so Muggles could never come and call - as if they'd ever wanted to - and now Dumbledore's added his protection, you'd be hard put to find a safer house anywhere. Dumbledore is Secret Keeper for the Order, you know - nobody can find Headquarters unless he tells them personally where it is - that note Moody showed you last night, that was from Dumbledore..."

(Harry Potter and the Order of the Phoenix, Chapter Six: The Noble and Most Ancient House of Black)

"Unplottable" means that Muggles can't see it - the way they can't see Hogwarts or any of the other Wizarding Schools - and the Fidelius Charm makes sure wizards can't see it either unless being told by the Secret Keeper.