Well, for starters you need to supervise her closely when she is free in the house. How much exercise is she getting? Basenjis need lots, and a tired dog is often a good dog. I assume you have chew toys for her, and you need to make it plain to her what she is allowed to chew and what is off limits. Consistency and vigilance are required with puppies and young dogs, be they Basenjis or any other breed. Bear in mind that Basenjis have a catlike attitude and prefer pleasing themselves, not you. It is necessary to make the wrong things difficult for her and the right things easy. If she is getting out of the crate, perhaps you need a crate of a different design or find an alternative way of securing it. Too much crate time isn't a good thing either. She should be tired when you confine her.
What is her history? You got her at four months…....from a breeder, or from a previous owner who had already begun to have problems?
As stated above, she should outgrow much of this behaviour, but I am a firm believer in not allowing the bad things to become a habit. You need a strategy for preventing that. Have you been taking her to training classes or working with her at home? How does she respond to training?