What does GLaDOS mean with “One day they woke me up”

GlaDOS is made up of a few different personalities (the personality spheres), and Caroline was probably one of the ones that was integrated closest to GlaDOS. It's fairly likely that Caroline's more closely integrated and influenced aspects of GlaDOS's development, but GlaDOS clearly has her own personality because otherwise she probably wouldn't have flooded the enrichment centre with a deadly neurotoxin.

There's a much simpler explanation for the turrets ignoring Chell; GlaDOS no longer wants to kill Chell, so the turrets no longer recognise her as a target. Because they're made by Aperture, though, they're quirky enough to recognise Chell as an audience instead. Hence the singing - you can run across them practising earlier in the game.

GlaDOS seems more interested in dividing Blue and Orange than picking favorites, and will show favor to either Blue or Orange. In the Yogscast, GlaDOS awards Orange "five science collaboration points" in one level (10:27 in), then awards the same to Blue in a later level (11:45 in):

In a later episode, GLaDOS states that:

• the challenge would present a challenge for one of the two given one's performance so far, but doesn't say who (0:00)
• the two form an excellent partnership with one handling the cerebral challenges and the other "ready to ponderously wander into action should the test suddenly become an eating contest", again doesn't say who is better (5:28)

But the smoking gun, as it were, that she doesn't necessarily favor Orange comes at 9:00 when she states:

To reiterate, this is not a competition. Still, if it were, Blue would be winning. [inaudible] Blue receives five science collaboration points.

So whether it's dependent on performance is possible (although unlikely if you watch these videos), but she doesn't seem to have a complete disdain for Blue.