I used to raise mantids when I was a kid. That looks like a nice healthy one you got there. Have you ever read about the mating behavior of the mantis? I'm glad I'm not a male mantis. =P
FWIW, my camera makes clicking and whining sounds too. I'm pretty sure it's the auto focus (infrared) locking onto objects at different distances. Fishtanks reflect the focus beam from the pane, which is why it doesn't whine as it's getting a solid return on the glass/acrylic and nothing inside the tank.