Disclaimer (as Mod): We are aware, that Tannheimer Tal is in Austria and this is the Germany forum. But given its location, I leave it here for now.
Regarding your question, I have been there but that has been more than ten years ago, tough I am not of great help.
If my memories are correct, the slopes are more blue to red rather than black level (there is only a short black one at Grän). I have not been to Schattwald myself (which is where the only black slopes is, but went to the Neunerköpfle region, as this ski area offered more routes than Schattwald and is higher. Looking now on
Startseite - Skifahren im Tannheimer Tal - Tirol I am not 100% sure, if the lifts were the same at this time, but I think so.
Could not recommed any ski school, as I did not use one. It was a quick one day trip after a business meeting in Munich ...