I got an uncommon item. Cannot remember exactly which one, but it was pretty cool. However that happened after I destroyed 10+ items and I believe I even got quite lucky. I think the chance to get one is quite low. All I can say is good luck bro xD
^ No. You only get items for destroying other items with qualities.
For destroying a common item theres a chance to get an uncommon item.
For destroying an uncommon item theres a chance to get a rare item.
You see how it works now I hope x)