Hi Basenji Luv… first, welcome to the forum, and more importantly, welcome to BASENJI life ! :) As you are learning.... first, basenjis aren't vindictive. He doesn't pee to get you mad, he pees because 1) he had to, or 2), he thinks he should. :) At his young age, if your mom realizes he's ready to go, she can interrupt his behavior with a loud "Uh Uh!"... or whatever noise she wants.... as long as she's willing to scoop him up, bring him outside, and reinforce, "go potty"... and then when he does, HIGH PRAISES!!!!
My husband wakes up before the world (4:00 am), and when the house is so quiet, he has trained the dogs to react to the sound of a ziploc bag opening. HELLO? Is that a stupid dog???? No, they know that if they hear that sound, there are rewards for the asking. Don't think that because he's little, he's not thinking... trust me, he is. :)
With that in mind, positive reinforcement for good behavior. When he squats outside of the pee-zone... scoop him up, bring him to the right place, and reiterate your magic phrase (i.e. "go potty"), until he tries to squat.
As for the nipping... there are 2 thoughts. First, if he bites you and you react loudly with an "OUCH!!!".... he may think you are a big squeaky toy, and bite again. (That's my girl!). If, when you react, he backs off, then he knows he hurt you and should back off with biting again.
If he thinks... "Cool, big squeaky toy!"... then you need to move him away from you. Don't make eye contact, don't encourage love. Be cold, if you can. This will send to him the message that good dogs don't bite.
(But they do go to heaven :) :)).
Hope this helps!