Looks a lot like my Jack. I haven’t done a DNA test because I don’t think it makes any difference. Jack is a rescue and I was told they suspected he was a Rat Terrier mix. My vet, too, says he sees some Basenji in him. He does bark but only when he feels threatened He gets my attention by making weird noises. He also grooms himself like a cat! He is very agile!!
Don't worry too much about the barking. Some do and some will remain silent for their entire lives. Barking is a continuous series of barks, and most Bs will do just one, without the continuing series of barks - like a lot of lonely dogs will do. He looks like he maybe a B, but you would need to get closer to his bloodlines, but does it matter? He looks like a good dog, and should be a keeper regardless of his pedigree.
To me, definitely a basenji mix. I have seen registered basenjis who are not square, 'curvy' topline. She is not as refined as a female basenji but that might be the mix showing up.
The howling noises are very basenji to me.
A few basenji characteristics she may/may not have:
Licks herself when wet, like a cat, does not have a doggy odor when wet, picks a particular time of day, and goes nuts, consistent with the time of day. Has a hard time controlling herself when a small critter, especially a rabbit is near.
Thinking she is part basenji will buy her a few 'oh well, that's the basenji part showing up' when she does something that a regular dog will get reprimanded for. With Lexi, roll up a newspaper and swat YOURSELF for not giving her a baseni proof environment!
Your life with Lexi will never be boring!
She's beautiful and looks like a tri-colour Basenji to me. One question no one has asked: does she have a freckled belly? That is a great trait to prove she has Basenji blood. Also, compare her paw pads to that of a wolf. How close are they? I am not certain with a mix they would match exactly as a Basenji does (they are the closest relative to the Wolf) but it would not hurt to look. Enjoy your beautiful girl.