Medallion Trigger: Very faintly, unless she's using gem magic--while Wave doesn't have any magic herself, she does carry an enchantment laid on her from just after birth (not that she knows it, nor would she believe it if she were told).
Scent: Juniper and a collection of different herbs, plants, and spices based on what she's been working on lately. He'll def be able to pick up poisonous scents from time to time like hemlock or nightshade sometimes :)
Pulse Detected (and description): Yep, and it's perfectly normal. He'll absolutely be able to tell when she's lying (if her face doesn't give it away first), and he may also notice her pulse jump if/when she uses her surname.
Gait/Breathing: Also normal! One thing he'll probably pick up on fast is that he'll be able to read her breathing just as easily as he can read her pulse. She's not great at hiding things.
Axii: Yes! Though as a heads up, if she realizes he's done it she's going to freak out :')