Hello! I wanted to share the growing "pains" that my husband and I have experienced with our little man that is very similar to yours. We've had our Basenji since he was seven weeks old and is now just over two years old. When he was a puppy and had his baby teeth, his biting was terrible. He bit us all the time, except when he was sleeping. And those little teeth were like razor blades. We were going through band-aids very quickly.
The breeder said that they pick up on biting when they are very young playing with their litter-mates. Even from a young age their play is somewhat focused on dominating the other siblings. The method to keep him from biting was to lightly clamp his muzzle with just your thumb and forefinger. Using your entire hand could cause too much pressure and hurt the sinus cavity. So we tried this method. It did not work.
We next consulted with our veterinarian. She recommended that when he tries to bite your hand, grab his lower jaw with your thumb on his tongue and hold it for a few seconds. He will try to resist and force your hand away to free his mouth. This technique worked okay and he appeared to actually think about it before he tried to bite. I assume knowing his mouth would be grabbed. This, unfortunately, did not completely stop the biting, but it was a start.
We continued to work with him but it was difficult to play with him without being bitten. He was determined to grab your hand when playing. After his baby teeth were replaced with adult teeth, which are quite large for such a small dog, the cuts to the our skin diminished. He still tried to bite, mostly during play, but the adult teeth bruised rather than cut. We have stopped all rough play and started enforcing our dominant role in the family. But it has taken a lot of time and patience working with him to stop biting. He still mouths a little when he is tired or wants attention, but he doesn't bite fiercely anymore. We didn't see real progress until he was about 14 months old. So patience is the key.
As for tearing up things like pillows and blankets and such, we wound up putting these things away or out of his reach until he learned to respect it. We've even taken away toys that he tried to tear apart and reintroduced them to him later under supervision. He has two small blankets that we have designated for him only and he has put holes each one. But he knows they are his and he seems to understand that because he has not even attempted to tear up anything else of ours. Except maybe socks if we leave them out where he can get to them. But I believe that goes back to when he was a puppy and we gave him a pair of old socks to play with.
Today, our little man loves to play fetch and lay at our feet and wants to be close to us most of the time. He knows a lot of commands, obeys them most of the time, especially if a treat is involved. He displays the typical Basenji aloofness when he doesn't get his way. But all-in-all he is a wonderful addition to our family. And the more mature he gets, he seems to be calmer, obeys better, and enjoys being with us.
Some other information about him - he was neutered at six months of age; he has a large fenced back yard to run around in; he was crate trained as a puppy but has not slept in his crate for almost four months (he sleeps on the fouton in our spare bedroom); he loves going for walks and meeting new people and other pets; and most of all, he is spoiled rotten.
I hope this is helpful information. My husband and I were very frustrated at first and it has taken almost two years to really get the biting completely under control. But we feel a Basenji is a great dog to have as a pet.
Good luck!