She digs small holes about 6-7 inches in diameter. Sometimes she buries things in there, other times it just seems she digs for the sake of digging, or is maybe sniffing out something under the ground. I haven't caught her in the act very often, but sometimes she does do it when I'm home and inside.
I've tried the trick of putting her own poo in the hole she's dug - she won't dig into that particular hole again, but she'll dig a new one!
Another thing she does is to sneak into the house if the door is open, grab something (any object such as a shoe, piece of paper or cloth, or small solid things), then she'll run outside and shred it to pieces. This is of course while I'm not looking!
She's also over-affectionate and if any guests show up, she'll jump all over them, stand up on two legs and paw at them, and won't leave them alone.
All in all she's a really naughty dog and needs a good balance of affection and discipline. She's still pretty much in a puppy mentality. I haven't had a dog in years so I don't really know how to handle them. Sometimes I see her looking up at me in a kind of 'ready' state and I can just tell she's saying "awaiting orders!".
Getting two dogs, I don't know about that idea at the moment because of the costs of feeding them. But it really does seem she's starved for the company of another dog. There's a German Shepherd next door and they always run up and down the fence trying to play with each other. One day my dog dug a tunnel under the fence and managed to get through to the other side. They had a ball for a while! They have made 3 attempted tunnels under the fence so far, trying to meet each other, with that one success. I've even seen them working on a tunnel together, each digging from their own side.