Wayward, thank you much. I thought about starting a new post but was so cited when I seen you had those books I just added my request onto that thread. Now to answer your questions:
No, the top of the curved section is not serrated. That is where it has been “compressed” as a result of being pounded on with another hammer I assume.
Yes, the bottom inside curve is sharpened to cut and the tip is sharpened to pierce.
And no, it is not a lathing or crating hammer and yes, I believe this is a completely factory original head.
Wayward, my guess is it was maybe made for use by a tinsmith or roofer for installing tin, copper or zinc roofing or flashing. The face of the head is identical to that of a lath hammer. Now whether or not it was made for that purpose but someone used it for like an “air chisel” like to cut lengthwise through sheet metal. That is just a guess though.
Following are the pictures you requested and I also included one of a lathe hammer I have (so others would know what we are talking about.) That old 1862 farm house I renovated had the “split & spread” lathe like this hammer was used for installing.