The answer to all three questions is ... sometimes it does, sometimes it don't.
Depth can play a part in not spooking fish, but that depends on other factors as well, such as water clarity & surface activity (like boat traffic, waves caused by wind, etc.).
The degree of spooking is also dependent on those same factors. You might "alert" the school of your presence, but not "spook" them away from the cover or area. Or you might cause them to seek deeper depths in the water column or the cover they're around. Then again, sometimes they just don't really react to your presence or the noise, one way or the other.