Congrat and welcome… She looks a bit like a Trindle (carrying the Brindle and Tri color pattern) then a Tri with what looks to be strips on her face... but a cutie regardless....
As far as eating, she will need some time to adjust, just give her a week or two and see if the upset tummy resolves itself...
You might want to read the links on Fanconi health testing and it would be a good idea to 1. print off Fanconi Protocol for her file at the Vets office in case he/she is not up to speed on this and 2. consider doing the DNA test to determine her DNA for getting Fanconi. There is a cheek swab test (cost is 65.00) and here is a link that you can learn about it. www.basenjihealth.org
Again welcome and thank you for opening your home to a Basenji in need, oh and as far as hearing impaired? Do you notice if her ears flick towards a sound, like calling her or if there is a loud noise? If the ears are reacting.. then could certainly be "select" hearing….