With that cross, you should have a smart dog. Whether she will be biddable like a Border Collie or an independent thinker like a Basenji will be interesting to find out. Great that she is good at the dog park, that should help with the physical exercise, but I would also challenge her mentally as much as I could. Keep her brain busy and she will be less likely to get into trouble. I recommend clicker training, and teaching her whatever things your imagination can come up with. I agree with crate training, at least until you have a handle on how trustworthy she will be.
You can train an incompatible behaviour to help with the jumping up, and if she is as smart as I think she is, it shouldn't be too hard to persuade her that using teeth when playing is a "no no". You can object verbally and cease the play whenever she does that, and see how she responds. If you are lucky that is all it will take, assuming you are consistent. I have some Border Collie experience, and they are 180 degrees different from Basenjis, so it will be interesting to see which traits are dominant!