Alright, so Skype it has requested it but the input does not register it in the app. Have you verified your input devices on your iMac?
To do this, click >System Preferences...>Sound>Input.
There, you can check if A) The built-in microphone is enabled and B) The microphone is receiving input. If it's not receiving anything and the mic is enabled, you'd likely need to take it to your local Apple Store, but I don't think that this is what's causing your issue.
My first suggestion is to uninstall and reinstall Skype. You can uninstall easily by going to Finder>Applications, dragging Skype to Trash, and emptying it.
However, you mentioned that Skype isn't the only program you're having issues with.
A good place to start in my opinion is resetting your NVRAM. This will not affect your personal data, and might solve some of the problems with your microphone.
If that doesn't work (Which is very much possible) try reinstalling macOS. This will also not affect your personal data and has a good chance at resolving the current problems you're experiencing.