Short,stiff hair
I asked this question!
I find that grooming like a horse is the best. A rubber bristled brush is best first. Then go over the body with a hard bristled body brush. lastly I use a soft bristled brush to brush away acess hair. I do this once a week usually. If your dog is really patient you can use a vaccum to go over them.
Toothbrush
a hard bristled brush and some cleaner, could be there forever though
Simply a towel and water, or a hard bristled brush for dried on muck.
Sounds like you have very sensitive gums. Try using a soft bristled toothbrush and make a visit to your dentist to be sure all is well.
The canopy
Use a stiff bristled brush and scrub it with soap and warm water - rinse thoroughly and let dry.
A small hard bristled brush on the end of a hanle about 200mm long for the cleaning of teeth, there are also electricaly run versions of this.
I would soak the paw in water for a few minuets and then go at it with a soft bristled tooth brush that is no longer in use.
Brush it off with a stiff bristled brush or if it's not too bad just tap it on a table or any other hard surface.
No makeup brushes are generally not as tough bristled. But paintbrushes can be used with makeup to achieve certain effects. The above is not completely true. Many synthetic bristled make up brushes are made with taklon (Urban Decay, Eco Tools etc) . Taklon also happens to be used to make a lot of paint brushes (Leow Cornell etc.)