iTunes automatically stops/starts music whenever I start/stop Skype call
iTunes has a separate volume control that seems to run independently of the master volume control. It's in the top-left corner, press ⌘↑ or ⌘↓ in iTunes to adjust.

Yours may be too low relative to the master volume.

Skype too has a separate volume control. In the Skype app press ⌥⌘↑ and ⌥⌘↓ to adjust call output volume only.