Formal training is definitely needed - but you need to find a trainer that is familiar with a number of different breeds (one of my first trainers was an aussie-shepherd person and never worked with hounds before - what a mistake that was).
If there are dog schools that offer the AKC Canine Good Citizen classes in your area, I'd consider these after you've taken basic obedience. Or ask about a "manners" class.
Forget the walks in crowded areas and forget the off-leash parks.
I also would not suggest the head-halters ("gentle leader") on basenjis - these dogs will suddenly "take off" towards a squirrel or other prey animal and the gentle-leader/head-halter can damage the neck (it works fine for dogs that are more people oriented).
Ditto Tanza's comments. Be consistent about taking him to potty (whether the litter box or ourside) and at regular intervals for now. When he does go, be sure to praise him (so he knows it's a good thing to go "when asked") and give a treat. Move the litter box to the doorway then to outside so he gets the idea - you can also train a particular area in the yard as well if desired. Always praise and or treat when he goes when you take him - that will help.
You might want to take advanced obedience classes - "mind your manners", "bogeyman", "impulse control" etc. if they are offered in your area
(Fenzi Dog Sports Academy offers such classes online also) or even a
competitive obedience novice level class. I found these sorts of classes
really helped my Teddy work more calmly around other dogs.
Never take mine to a groomer - as Tanza said they pretty much self groom - I brush in spring when their winter coat comes off. Quality food and maybe some fish oil supplement will help. If his skin is really dry you may need a shampoo (oatmeal based recommended by my vet).
Mine get RedBarn ChewyBulls - totally digestable - or other dental type chews (never rawhides - I found a 3 inch stick of rawhide in their poop - never understood how it got through without doing damage - never again).
They also have Nyla bones (until the edges get too sharp) and occasionally bully sticks (fat ones only) or regular marrow bones (thick cut).
I used to use antlers until a friend's dog broke several teeth on antler.
I see both good and bad to raw diets exclusively. As long as you provide a well-balanced diet (vitamins, minerals, veggies, meat and organs) I see no problem. If your dog is healthy why change.
There are also good and bad kibble diets. A great source of kibble evaluation is the February issue of Whole Dog Journal, where they evaluated a large number of kibble diets based on ingredients, protein quality, etc.
My dogs live on kibble with canned food, raw patties (usually pheasant, fish, or venison), or veggies (beans, peas broccolis, carrots, sweet potatoe) added as topping. They also get apples, melon, blueberries as treats along with commercial treats.
If your dog is healthy and teeth are good, then whatever diet you are using is the right one.
I made fleece coats for my two - but really they don't go outside except to potty when it gets real cold (this winter we often had days below 0).
They never wear booties - don't stay on long enough - by the time I got the last two on, the first two would be pulled off !
For starters, treats should be good quality and low calorie.
I always used special treats for different activities. For example, treats I used in obedience class had to be high quality to counteract class distractions (often I took cheese) but treats for home practice could be simple Zuke minis. Treats that I use for recall rewards I never give any other time.
Never use the crate as "punishment" - even if it is for "time out" give a treat - always make it a happy place. My dogs get a biscuit for crate time and never get that biscuit for any thing else.
Yes it means I have bags of different treats around (yee gads).
Additionally treats have to be gradually removed with lots of praise substituted. If you do clicker training, this will go a lot easier.
Most importantly, the sudden change in behavior could signal a medical issue. Perhaps a tooth has gone bad. Check with your vet.