Is she spayed? It is "breeding season" and if she's going into heat it might be causing some changes in her behavior.
I totally understand the frustration you feel with her classes. At my dogs first class we all went around in a circle and introduced our dogs and shared what our plans were and I said I wanted to work on his focus, leash training and hopefully try agility and they laughed and told me "good luck with that!". Well.. I'm paying you to show me how to train my dog, I can tell you don't like his breed and I'm already unimpressed with the first class. He does well in class with toys (he doesn't care for food). Have you tried a squeaky toy to get her attention? I also play with him during the down time to keep him excited about class. I keep a few super fun toys in his training bag so he only gets them during class. Even with a toy he loves I can see him getting bored after a half hour. He does the exaggerated basenji yawn, starts to chew his lead, climbs all over me and stops listening. I've considered leaving early so we end on a good note but of course they go over "homework" at the end of class. Something I discovered while out on walks and he's ignoring me (my voice) because of a good smell is that if I stomp my foot I can get his attention. He looks up at me, I praise him and we move along. I know he will never walk next to me at full attention but I love that now I can at least get him to acknoedge me and I can get him under control. Still work on it each day!
The cat thing is tricky. I have 2 cats who have lived with 2 different basenjis. One cat just sits there and takes it when the basenjis "play" with him and they didn't/don't view him as prey. My other cat runs, hisses, swats and pretty much hates the dog. It's MUCH harder with her because she makes herself seem like prey and thus a hunting dog with strong prey drive wants to chase. He has never really tried to hurt her but I still have our house set up so the cats have areas where they are 100% safe. Cat trees, baby gates, closed off areas, etc. While you are training her you NEED to give the cat somewhere to feel safe. My cats know what the sound of his kennel closing is and my female cat comes into the kitchen with in minutes of Elliot going "night night".
I would think about doing daycare more frequently if you can. I work at a vet and dogs/puppies that go to daycare are almost always easier to work with because they are so well socialized. We just had a puppy in for her spay and I complemented her owner on her perfect behavior and she told me that the puppy goes to day care or to work with her almost daily. She sees a ton of people and dogs so nothing is scary or threatening to her. Not saying it's a miracle cure but I can't overlook the good results I've seen.
She's not /quite/ old enough for it yet but the best energy drainer I've found for my dog is the bike. I have the Walk Dog bite attachment and with the right harness and a little training he LOVES it. Sees the bike and starts spinning and tries to put the harness on himself. He runs full speed for about 15-20 minutes and then sleeps all afternoon! He is 2 years old, in good heath and body condition and we slowly worked up to that much exercise. I also walk him to cool down afterward and make sure he doesn't drink too much water right away.
I'm sorry your breeder can't help you. I don't know what I would do with out mine! He's always been able to help me with everything, including serious illness. I too have days where I work all day but I'm lucky my parents don't work as long of hours so the most he's alone is 5 hours.
I don't have much advise on the biting. Mine never did anything more than a little puppy biting and I'd just redirect or walk away. I might be wrong but I've seen basenjis play roughly and I've seen them kill small animals (squirrels, rabbits, etc) and the screaming the other animal does seem to make them continue to "attack" harder. My cat is the master of "ignore the dog and he will go away" and it works! Elliot puppy bit my mom for a long time because she'd scream and carry on and once I got her to stop.. he stopped. If it's as serious as you are making it seem I would look into a behaviorist.
I hope my giant jumbled post helps a little. I can tell how much you love your baby and want this to work out. Don't give up!