As said check the wiring on the alternator. The thin blue wire is what you will be looking at. A certain member on here recently also proved the theory if you bolt the main charging cable to the BLOCK the light will stay on aswell (you know who you are )

As for the idling fault..............one that springs to mind, it may sound dumb..........have you even got an alternator belt on there! If the belt was to snap it would idle high seeing as there is no idle speed compensation, and would explain your alternator light also.

If the belt is all good, there will probably be a problem with your auxiliary air device