They can do well in a small house, but need walks AND exploration AND interaction with other dogs. Movement is not enough, you need to let them use their mind. When on leash our 2 sisters can sniff all they want, even if it means we do one mile in an hour. They will be tired afterwards.
Trainability: depends on the individual, the age, the human. On YouTube or dedicated fb-pages you can find basenjis showing perfect obedience, even stunningly choreographed doggy dance routines. Will take time and effort and patience. We found that if we treat them along the lines of how you would interact with a 3 year old child, all goes well (most of the times anyway).
Maybe something happened to him before he came to live with you - a male that did bad stuff to him? Do you know anything about his previous life? For now, I would leave him alone, be very calm and talk in a quiet voice, both you and the guests, and ignore him. No treats, no touch, no eye contact, no words, no direct body language in his direction, no big arm movements - hopefully he will start to pick up that all is well and quiet and that he can feel safe enough to be calm himself. All the best.
That's the spirit! If you cannot get enough of this kind of images, and you are on facebook, check this page out: https://www.facebook.com/groups/basenji.international/ Almost 9.000 members from all over the world. More than your daily dose of B-cuteness.
We are lucky to live in an area (Netherlands) where we can buy good quality raw (deep frozen) food, with good balance between muscle, bone and organs. Also lots of varieties are available. Why would a raw diet be odd? What would basenjis eat in the wild? Meat, eggs and plants. So we feed meat, eggs (one a week) and vegetables (raw/cooked broccoli, carrot, beet, cauliflower, beans and the like). No rice, no peanut butter. Pumpkin only in case of stomach / digestive trouble. No kibble.
I found that when I have little time, I let our two sisters sniff around all they like. It engages their whole being, including their easily overexcited B-brains. When I thake them back in after half an hour they will sleep all day. Running is fine, but it does nothing for their brain or their instinctive need to explore their surroundings. If pressed for time, I would choose sniffing over jogging or biking any time.