Getting the Overclocker achievement in Portal 2

The moment you enter the room, a script is activated which kills you when the room is flooded, regardless of whether you're in it or not.

This means that even if there were a way to escape it, you would still die.

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.