Hi - a few thoughts in case they are helpful, although ours doesn't bite.
For biting:
Figure out the reasons for biting first.
if it is around toys/possessiveness - we gave him the toy on his bed and let him be there gnawing on his own. Then walked close by (not too close) and threw him something yummier in his view (eg a small piece of sausage that he can eat quickly) and walk away. Do this at random (though not too often) and have different people in your family do it. Soon she will associate your coming close to her and her favorite toy as something good. Progressively get closer (ie throw the sausage from closer), and then squat down, then touch on head briefly, then hand sausage to her, then move hand towards toy but don't touch it. By this time she will anticipate your coming to her when she has a toy as "yay, something more tasty coming my way". Evenutally, you should pick up the toy/bone hand her the sausage then hand back the toy/bone. Pretty soon she'll let you pick up her toy/bone without biting or thinking you are going to take it away. The key is to progress slowly in terms of distance etc, and mix up the treats (sausage, cheese, chicken).
-if she does bite someone, then immediately isolate her in a basenji-proof room where she cant destroy things. And when letting her out, ask her to sit and be calm for a few seconds first so that she's not hysterical and she learns to watch and listen to you. There may be something else that one does for biting, so maybe others or a trainer would have good ideas.
For pulling on walks, 2 things worked for us:
A gentle leader - suggested by our trainer. This means she can't control her head (if they pull forward their head moves to the side like a horses halter) and so she won't be able to forge ahead. It will give your arm/shoulder immediate relief while you work on the rest.
In the yard and on walks start rewarding with small treats every time she looks back at you/checks on you. At first she'll do it by chance, or if she is checking to see what you are doing, and sometimes it's a side glance. As soon as she does it - give big verbal praise and get her to come to you and give her a treat and lots of pets. She will begin to do this more often. initially treat every time she looks at you, and once she is good at it, then randomly. On walks you'll find her looking back and coming back to you more often, and as a corollary less pulling, which is a relief. We usually keep the leash in one hand and a handful of small, soft treats in the other - so you don't run out and have to keep going into your pocket to get treats. So, she'll come and nose your hand and you can pet some times, treat sometimes, etc.
The one thing is to progress slowly, praise the right behavior and don't get impatient (count to 10, stop training or go do something else for a bit till you feel ready to try again). When doing the praise really have an excited voice and go overboard even! Our basenji really loves being praised. It takes more time perhaps than other methods, but it's long lasting because they see these behaviors as rewarding so you don't have to get into a battle of wills. And once they get the idea, they'll improve rapidly, even over one walk.
Good luck!
The trick is to make the dog want to please you, not so easy with a dog that really doesn't give a rat's patootie whether you are happy with his behaviour or not. (granted, some Basenjis are more interested in pleasing you than others, but "biddable" is not a Basenji strong point!) Food rewards work well for Basenjis, but aren't the answer to all problems. I do believe in letting the dog know there are consequences when he crosses the line. (of course, he must have a clear understanding of where the line is!)
