How did Kreacher know that Lupin was a werewolf and Hermione was a muggle-born?

Question

When Harry first met Kreacher, he was muttering under his breath but that was a very audible muttering.

oh, my poor mistress, if she knew, if she knew the scum they've let into her house, what would she say to old Kreacher, oh, the shame of it, Mudbloods and werewolves and traitors and thieves, poor old Kreacher, what can he do....'

^{Harry Potter and the Order of the Phoenix, Chapter 6 - The Noble and Most Ancient House of Black}

then he said to Hermione

'The Mudblood is talking to Kreacher as though she is my friend, if Kreacher's mistress saw him in such company, oh, what would she say--'

However, Kreacher was present at the headquarters of the order, but things like Lupin being a werewolf were only discussed in meetings. So how did he found that out? Moreover, Hermione being a muggle-born was not even a subject to come around as most of the order people don't know her and those who knew her don't care less to mention it. So how was Kreacher getting the information for his muttering?

Answer 1

Hermione

Her name alone would have been enough for Kreacher to know that she's not a Pureblood. Kreacher served the Black family, a prominent and extremely proud Pureblood family. They would know all of the other Pureblood families, and therefore Kreacher would as well. There's even the Black family tree painted in one of the rooms, and the limited number of actual Pureblood families remaining means that the Black family tree also includes at least parts of every other Pureblood family as well.

Lupin

There are a few possible ways for Kreacher to have discovered this information, though they all essentially come down to the continued theme throughout the books of (most) witches and wizards not caring much for, or about, House Elves.

He's an old House Elf who has served the Black family for a long time, including when Sirius still lived at home while attending Hogwarts. Kreacher may have learned about Lupin being a werewolf as long ago as that, if Sirius had been discussing it at any point when Kreacher might hear.

Otherwise, the Order didn't seem that concerned about the security of meetings within Grimmauld Place, so it's not inconceivable that Kreacher simply overheard this fact during one of them. They removed the children from meetings when they occurred, but the Weasley twins were still able to spy on at least some of them. They also believed Kreacher wouldn't be able to reveal any information as he's magically bound to his master, Sirius, so would perhaps not be too concerned about him hearing things.