Training a Basenji can be difficult. There are a lot of variables to take into context though. (You got luck guys) I have one line that would be pretty reliable and are more attached to me. However, my other line simply does not acknowledge I exist at times. So that line, I would say, would be unreliable. There are people out there who breed specifically for certain traits, such as hunting, tracking, sporting, etc. So if you are looking, please remember when selecting a breeder to search out the ones that specifically breed for the traits you want.
Personally, when I was training my boy for Rally Obedience, I found that if I moved quick enough, he focused on me rather than what was going on outside the ring-again this is from the more reliable line.
Some Basenji's are fine with cats-others not so much. Three of mine (again, the more reliable line) are okay with my cat, the other line, I wouldn't trust with a 10 foot pole.
All of my basenji's are good with kids. Shadow was older when my grandson came along and is fine with him, as are all the other basenji's that I have. They have been raised with kids and are used to them.
Basenji's can, and do, do well with training, they just need to get past the boredom factor. I would love to have more time to do more obedience and agility with my kids, unfortunately, this is not the time. But it can be done. My opinion only.