Omniscient Dumbledore /Snape's guilt

[houyhnhnm102]

No: HPFGUIDX 135701


Alla:
 
But that is the big question to me. Did they have a lot of those 
private discussions over the years, or we just assumed it, 
imagining  that Snape is DD right hand man?

houyhnhnm:

In chapter 2 of HBP we are shown what Snape has been telling Voldemort
and the DEs.  We are never shown explicitly what information Snape has
passed to the Order, but I think there is indirect evidence, in
chapter twenty-three of HBP, that Snape and Dumbledore have a
confidential relationship and that Snape has passed on a great deal of
critical information.

"'I wonder what you will say when I confess that I have been curious
for a while about the behavior of the snake, Nagini?'
...
'I think he is perhaps as fond of her as he can be of anything; he
certainly seems to keep her close, and he seems to have an unusual
amount of control over her, even for a Parselmouth.'"

and 

"'...but [Voldemort] was not aware, for instance, that the diary had
been destroyed until he forced the truth out of Lucius Malfoy.  When
Voldemort discovered that the diary had been mutilated and robbed of
all its powers, I am told that his anger was terrible to behold.'"

How else would Dumbledore know these things except from Snape?