Hello vitchee, and Welcome to Linux Mint. Unfortunately skype is a proprietary program which does not work exceedingly well under linux, e.g. I've found it doesn't work while flash is playing in firefox. The solution will largely depend on your hardware (post the output of the inxi command) and what's available in the drop-down list in the Sound settings. Do you get the "Cannot connect to sound server" error, or "Problem with audio playback"? How do you know the microphone isn't working, have you tested it with the echo service? Have you disabled the "allow skype to alter mixer levels" setting? You might also have the microphone muted, which you can check in the main volume control preferences. Other than knowing the more specific information, I'd basically try every sound setting combination you can within skype.
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