Hello Valyti, I am from Italy, and I have applied for the short term. I am still waiting for the results, and I've applied in September (and now again in April). Still no results for the first one...
Anyway, I spoke to the Italian DAAD centre, and the wait for the final results of the short term application is generally at least four months. Before that, you will receive a message if your application is complete and considered in the selection process.
I hope that is helpful.