#1 sounds like a fear reaction, especially the expressing of the anal glands. Her aggression is her trying to defend herself. The only fix for this (other than tranquilizers) in my opinion is taking a lot of time to make her comfortable and less defensive with basic procedures. Was she a puppy when you got her or a rescue? If the latter, there may be some history you don't know about. I would work with her at home, gently but firmly and with lots of rewards for good behaviour. There should be no areas of her body that you cannot touch. Be patient and preferably work alone. Dogs (and other animals) do not like being "ganged up on". Gain her confidence one step at a time. Make very sure that nothing you do hurts! Work on being able to handle her feet, and eventually clipping her toenails, but take it very slowly and reward for any progress. And work with her daily for short sessions. DO NOT BE CONFRONTATIONAL! Firm, yes, but very "matter of fact". When you get to the point where you can handle her all over and do basic grooming tasks, then it's time to introduce someone else under your supervision. She may not get over her aversion to vets. Face it, the dog knows where it is from the smell, even if they have not been to that particular clinic, so a muzzle may be necessary to ensure the vet's safety. Buy one and get her used to wearing it for short periods at home. Put it on her just before you go into the office with her, not after she is already all tensed up.
If you must force the nail clipping, wrap her in a large towel (works with cats) to avoid those scratches and "bear hug" her as gently as possible. If you can walk her on pavement you may not need to trim nails very often.
#2 Not unusual. It isn't affection, IMO. Basenjis can be very intent on "cleaning", themselves or others.
#3 Again, pretty normal for a Basenji. Try a martingale collar and try reversing direction when she pulls. Not moving forward when she is pulling is a good strategy if you have the patience for it. Not everyone does!