This is a feature in Skype sometimes referred to as Integrated Calling, in which the Skype app diverts calls which you had intended to go through FaceTime. It has long troubled iPhone users; it can now be disabled on iOS/ iPadOS devices. On the Mac, its equivalent is a control tucked away in FaceTime’s preferences, and it appears that Skype may change this for you when it’s installed.
Open the FaceTime app’s Preferences dialog and select its Settings tab. At the bottom is a menu to set Default for calls; change that from Skype.app to FaceTime.app, and you should be able to use Skype, Messages and FaceTime properly. If not, try signing out of Skype first, then change that preference setting in FaceTime. Older versions of the Skype app could also be more difficult, but if you’re running the current release (8.81 or later) and still can’t disable Integrated Calling, then you may be forced to make a choice between using Skype and uninstalling it altogether.