To the first the questions - yes. This problem has been going on for a long time now.
I can't activate Hey Siri, because the microphone doesn't pick up anything in the set up process of Hey Siri.
The 3-4 second delay occurs when I use Siri, when I send voice messages via iMessage (but not via other apps), and when I'm recording a video with the FaceTime camera. I am presuming that all of these use the same microphone.
The confusing part is the delay, because otherwise the microphone works just normally, it just needs time to start picking up the sound (the time is always the same, between 3 to 4 seconds, as I stated above).