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Yes. Dogs and cats can be right pawed or left pawed. You can test to see which one yours is by placing a tube directly in front of it and put food in the middle of the tube to see which one yours is.
Yes. Male dogs that are not castrated usually prefer the left paw. Females not castrated prefer the right. Hormones will effect the paw preference. Once the dog is spayed/neutered it changes.
I'm not aware of how scientists determine paw preference, but as a dog trainer for ten years I have two methods that seem to work:The most reliable is also the simplest. First, take a treat and hold...