Can a general aviation aircraft be forced to land when crossing the airspace of a country?
So in order to take your plane for a flight, you have to file a flight plan


Usually incorrect. Flight plans are only needed for international and for IFR flights. But there are some countries where a FPLN is required for every flight, but not Italy, Austria or Germany.


  when you are flying you have to, using the radio, let them know that you are on your way


Only if you've filed a Flight Plan. If you haven't, then there's no need to announce your flight.


  Can the Austrians ask me to land in their country for any reason


They can, it's their country. But unless you're a criminal or a terrorist, there's probably no reason for them to actually do this.


  Will they shoot me down if I don’t comply with them and land in Austria?


If they ask you to land (see above) and you don't, then they could shoot you down. It's their country and they're trying to protect it. But it hasn't happened yet.