I'm glad you are doing some research before running out and getting the first Basenji that you can... but, a lot of your questions can't be answered: I'm pretty sure that none of us can see the future... None of us can tell you if you are going to be allergic to a Basenji, or if your dog is going to keep you awake at night, or if your dog is going to chew (specifically) the electrical cords (btw, puppies chew everything), or if your dog will annoy your neighbors.
But, you can control much of this.
@tanza is right, visit someone who has Basenji's and find out if you are allergic to them. Check with your local Kennel Club, Veteranarians, or Dog Trainers -- it's almost certain that you will find someone who can help you find out if you are or aren't allergic to this breed.
Be prepared to wake up during the night (at first). Puppies have small bladders. A midnight dash outside shouldn't be unexpected. Decide now if your dog will be welcome to sleep on the bed, on a dog bed nearby, or in a crate. Puppies are quieter when they sleep with you. If you choose a crate, place a blanket over it when it's bedtime. If it's a dog bed.... put one of your dirty gym shirts on it so the pup can smell you and feel like you are nearby. (You might not get that shirt back)
Chewing? Yep, puppies chew. Keep your place clean. Put your shoes in the bedroom closet. Then close the door. Pay attention. If your dog is showing curiousity about something they shouldn't be messing with, very firmly, say "no!". You do not have to strike the pup, or yell at them. A firm "no!" is usually enough. Then distract the pup by providing a toy or a game that is okay.
Is your dog going to annoy the neighbors? Most certainly! Your neighbors are going to be beside themselves with questions about this little pup. I have people pull up alongside me at traffic lights, "What kind of dog is that? How do you spell that? Is the breeder local?" OMGosh! Has no one else discovered "Google"? Noise is the least of your concerns.
Whatever breed you end up with... give your dog attention, exercise, good food, plenty of water, and make sure that it feels loved and safe.