Sorry for the many images.
I rewatched the trailer and I made some observations.
As you can see, the three holes on the axe are smaller than the first one which contains that yellow thing. I think the other holes are for upgrades, because of their smaller size. However, maybe we can switch the yellow thing with a different color thing of different power.
Kratos has a sword, too. Check the left side of axe's bottom.
Fire demon?
Runes. I tried to translate them, but the translated text made no sense.
There runes on the horn, too. I think the text means south or it has something to do with south (a nod to Kratos' origin, perhaps, Greece is in the southern part of Europe). Take this with a grain of salt, though.