Is it possible for any given android app that has granted certain permissions (like for exampleViber - network access, file storage, microphone...) activate microphone whenever app is running even in background and listen to sounds in external environment (like conversations of people near phone), and is it possible when phone is locked (phone is one but not in use)? Please provide evidence for any claim.
It is. Look at Google's search app. If you install 'Google Now' you can search using your voice from the lockscreen after giving the trigger phrase 'Ok Google' (if you've configured it and taught Google your voice).