Is there any scientific process to verify if weapons such as this have been used in battle?
Sure! Both visual and microscopic analysis make it possible to identify wear or use marks on the surface of the blade which suggest its use.
So how many people would you estimate this thing murdered?
Unfortunately, there is no scientific process to begin to approximate the number of people that "came into contact" with this weapon.
Were there wars or battles taking place during this axe’s period?
I'm sure there were! Some of the conflicts taking place in Egypt around this time include Seti's military campaigns in Asia, Libya, and Nubia and attacks from Libyans after the Bronze Age collapse and subsequent collapse of the New Kingdom.