Vicks Vapor Rub is poisonous to humans if digested, I would suspect it's the same for dogs. So I wouldn't use it on a dog.
Yes, it is.
No, dogs do not use language of any kind. They communicate in other ways.
Yes, it is.
put gloves on the dogs paws
Don't know about dogs. Cats are ambidextrous. They use the L and R paws equally.
Yes. If it still smells strong enough to work, use it! It's not taken internally, so nothing to worry about except lack of effectiveness.
Vick's vapour rub is not formulated to be rubbed on a burn, and may sting. Only use medication formulated to be used on a burn - if in doubt, ask a chemist or your doctor.
if your dogs feet are muddy just simply try and use a cloth that you never use and wipe his feet.
I am not aware of any test that looks for the ingredients in Vicks vapor rub, so I can't see how it could possibly cause you to fail a drug test. If you're exceptionally paranoid about it, tell the person administering the test that you used Vicks vapor rub and you want to make sure it won't interfere with anything. This person has to watch people pee in a cup all day, they could probably use a laugh.
They don't have a left or right paw (they do but you know wht I mean) they use all their paws to do work.
Usually it is the lioness that hunts. They use their paws to chase down the prey. Sometimes they use their paws for the kill. Sometimes they use their jaws.