How does Camille walk?

Very carefully.

The same way Elise does on her two (or eight) pointy feet. Like a boss. Or very carefully.

She walks on knives edge

Does she walk? Whenever I see her she's either flying around from walls or leaping to the ADC.

With programming, she simply types in exactly where she wants to go, and her legs auto adjust so she doesn't fall over, that's how great she is at planning, she knows every single thing she'll do in game before hand, even her own deaths, and tells her legs to do it all before the game even starts, she's on constant autopilot, she could probably take a nap while it's all going on.