No I don't know where Zuko's mom is.
But I do know how Aang got into the avatar state and why katara wasn't a factor and how the rock in his back makes sense.
So, Aang left the guru and the guru said until Aang unlocks his last chakra he wont be able to go into the avatar state. then in "Crossroads of Destiny", Aang is losing badly and goes into the crystal teepee, turning his back on Katara, then he unlocks his final chakra and masters the avatar state (yes Mike and Bryan even said so in the comentary of "Crossroads of Destiny") then Aang gets hit by lightning, Aang dies, but then is brought back to life by Katara and her spirit water. In "The Awakening", katara says there is a lot of twisted up energy in Aang's wound. Back in the escape from the spirit world online comic, Yangchen says that Aang's spirit is ok but his phisical body needs healing and by this she means that until the energy twisted up in Aang's back is put into place he wont be able to go into the avatar state. now in the finale Aang gets pushed into the rock with so much force that it rearanges and straightens the energy in his back, giving him access to the avatar state. But, because Aang is in so much danger he is forced into the avatar state, which is why he didn't have complete control of himself while he was in the avatar state, he only had enough control to get himself out (note: Aang only has complete control of his body while in the avatar state if he puts himself into it).
So, Aang already opened his final chakra and mastered the avatar state before the finale, the avatar state just wasn't available to him. (I'm sure all of you have season two box set, or at least all of the dvd volumes, watch "Crossroads of Destiny" with the comentary on)
Also, Aang can be in love with katara and have a family and everything, he just has to put the world before his family and all attachments, this is what the seventh chakra means. (proof of this is Avatar Roku and his family in "The Avatar and The Firelord)
But what about in "The Invasion" when Aang says his seventh chakra is locked? Well, it was either a poor choice of words only meaning that you cant go into the avatar state, a mistake (eek! I hope not), or when you're energy gets twisted while in the avatar state, your last chakra just gets locked autamatically until the energy can flow correctly through it again.
People not knowing or understanding this have often changed their oppinions on the finale, and a lot of people think the rock in aangs back is what made him master the avatar state(no no no), so I just wanted to let people who were confused about the finale get the answers they want... besides the answer to the popular question "where's Zuko's mom?"...