One thing you can do regarding the "shredding everything" is to re-direct your puppy to some other activity when he starts to shred something. Kipawa does like pillows, but so far none have been chewed or shredded because where the pillows "live" (couch, chairs and bed) I keep one or two toys available. I show these to Kipawa right when he starts to chew/shred something he is not allowed to, I squeak it or wave it around, and he immediately gets interested in what I am showing him. This requires keeping a close eye on your dog though. But it does work. And you can limit the rooms he chews/shreds in by closing doors. Kipawa does not have access to our bedrooms, and we use baby gates as well to confine him to areas that we are in, so that we can supervise.
I don't know the age of your daughter, but get her involved in these tasks as well. She will feel a sense of pride and accomplishment when she is able to be an active part in your basenji's training.
And Pat is 100% correct about not leaving things laying around. A basenji will see these things as "fair game", because in their minds if you left it laying around, you must have meant for them to play with them. I slipped up on leaving a pair of shoes on the floor and suffered the consequences. There is now nothing on the floor, ever.