What you have to do is take her outside and let her go like u said. When >>she doesnt go outside bring her in.
I would suggest NOT bringing her in if she doesn't go outside. Do NOT bring her in UNTIL she goes potty outside. When she does go – and it may take a while -- praise her heavily "Good potty!!!, etc, THEN bring her in the house.
If possible, Take her out every 40 - 60 minutes or so, with a cheery "come on! Let's go potty!!" And heavy excited praise when she goes.
For accidents in the house -- if you don't see it happening, just clean it up as quickly as possible without any fuss. Use cleaners {white vinegar, enzyme solutions, whatever you have} to get the smell out. If you see her about to potty {or if she's just finished}, Say, "NO!!!" and run her outside as quickly as possible.
When you see her sniffing around the cupboards, firmly tell her "Leave it!", and remove her from the area. You may consider standing in front of the cupboards, and every time she attempts to approach, simply move your body to present a block and take a step toward her -- sort of pushing her off w/out even touching or speaking. You'll be "claiming" those things as yours. Maybe snap your fingers to get her attention, eventually you will probably be able to keep her away from them by simply snapping your fingers if she heads toward the kitchen.
Crate her if you can't be with her -- when you are gone, taking a shower, etc.
Keep the bathroom doors shut.
The key with a Basenji is to be infinitely patient, and CONSISTENT. It takes some time, but with gentle but firm consistency {I don't recommend hitting a dog, or rubbing their noses in messes they make} you will have a dog that you can live in peace with.