Hi,
You have 2 issues here, digging and stealing and chewing up things. About the digging, I have heard that digging pits help a lot with the problem. How this works is you pick a spot in your yard that she is allowed to dig in, and what you do is burry things in the pit, treats, bones, toys, anything you can think of you, put them in different places in her pit at different depths, start out shallow so she gets the idea. Somestimes she gets huge jack pot in her pit and sometimes it is just few cookies. She never knows but it should discourage her from digging in other places in the yard, where there is no reward at all.

About stealing things in your house, remember she is a puppy and even at 6 months still needs constant surpervision. If you can't be watching her then I suggest you put her in a crate with a bone or something to do. Exercise will help. How do you react when she steals things? Do you make a big deal about it or do you just walk up to her and take it away? When my puppy steals something, I walk up to her take it away and say no. That's it, not a big fuss just calmly take it away.
Good luck and let us know how it goes.