Wow! These are spectacular! I love all of the designs but especially the third from the left, which is something I've never seen the likes of before.... a serrated axe. It looks absolutely terrifying. One thing that interests me however is that you wanted them to be inspired by or have the feel of an ancient South American feel [Mayan/Aztec/Pre-Columbian] but as far as I know the ancient South American peoples didn't have any weapons grade metals until Medieval times. They used to make their weapons out of razor sharp obsidian.
It would be cool to see you redesign these with obsidian blades. :)
If you're interested, check out this obsidian Mayan axe Head:
https://assets.catawiki.nl/assets/2015/6/16/a/9/2/a925f478-1455-11e5-8a2a-e0ed23d5109c.jpg
Myan knife
Aztec Knife: