If you have configured the scales correctly (ie zero-ed them out properly) and are weighing the racquet WITH THE CARD attached then 325g isn't out of the ordinary. It would be good if you could weigh the racquet without the card attached to the hoop but I understand that might not be possible. (I weighed a similar card and it was in the order of 20 grams, so if you allow 20gs then it brings your racquet into spec. The plastic wrap over the grip adds a little weight as does the plastic that holds the card to the hoop.)
I have several 2013 APDs bought over the past three years. All of mine have Serial Codes starting with KH. If you look at the GT Stickers on mine, while they all have the "Graphite" and "Tungsten" words on the labels, the stickers are in slightly different positions depending on the grip size. I have APDs in different grip sizes. However, all the sticker on racquets of the same grip size match perfectly. I do not have any 4 1/8 grip size racquets though, so it is possible the labels on those dropped the words "Graphite" and "Tungsten". On all of my racquets the "Made In China" logo is printed on a 45 degree angle rather than at right angles to the the throat.
It would also be nice to know what the Balance is. How does it swing with the card attached? It should feel a little Head Heavy if you swing it slowly. Don't swing it fast with the card attached because the wind resistance will give you a false perception. If you swing it slowly and it feels very very head heavy then you may have a fake.
Looking at all of your photos and allowing for the slight color variation my initial guess is that your racquet is genuine. But it is hard to say without actually looking at it in the flesh.
Ideally, see if you can get your hands on another 4 1/8 size racquet at an Authorised Babolat Retailer and do a direct comparison.
