He needs to be crated when you're not home to monitor him. For his safety and your sanity.
Some folks will be along with more direct advice. Maybe NILIF would help. I had to keep my rescue crated for a couple of years when I wasn't home. Got him as an adult rescue too.
A good trainer, one that works with GSDs may help you work through these and the other issues more efficiently.
Smitty (rescue) Ilda WGSL 4/28/10 Autumn Australian Shepherd 10/9/11 Stihl Bonafide von Nadar WGSL 3/23/15