I recently purchased a Sony 70-200 F4 and have been testing it on my A7 (the very first one). I noticed that there's a clicking sound and the display (both in the LCD and EVF) flickers whenever I change the aperture value. I'm guessing this is because of the aperture blades, but the thing that's been bothering me is that there's no clicking sound nor flickering display when I'm using my other lenses - the 24-105 and the 28-70 kit lens. Is this normal?
I also noticed that the AF is quite poor when shooting in low contrast or low light situations. Not too low though, like the soft light of the sky during golden hour. Anyone else experiencing this?
The "clicking" sounds you are hearing is almost certainly the OSS (Optical SteadyShot) mechanism in the lens. Lenses from pretty much all manufacturers that include lens based optical stabilization make similar noises when starting up or when compensating for camera/lens movement.
Your 24-105 and 28-70 lenses do not have OSS, as the IBIS system inside many Sony cameras is sufficient at those focal length ranges. At longer focal lengths, though, the same amount of camera movement results in a larger displacement of the subject as a percentage of the frame size. IBIS is limited in terms of range of motion by the size of the image circle projected by the lens as well as size and space constraints inside the camera body. Thus Sony has added OSS to the longer Sony FE 70-200mm f/4 G OSS telephoto lens to supplement IBIS.