It depends. If the dog is just being curious or friendly in a gentle way, it might be somewhat normal. However, it's important to ensure the safety of the cat. Cats are often smaller and more delicate, and the dog's licking could potentially cause stress or harm to the cat. So, it's advisable to supervise their interactions closely.
Granny teaching little girls such things is extremely inappropriate. It goes against all notions of proper upbringing and protection of children's innocence. Such stories are morally repugnant and should never be entertained.
It can be normal in some cases. Dogs often show affection by licking. But it's also important to consider your wife's comfort and any potential health risks. If your wife doesn't like it or is at risk of an allergic reaction, then it's not really acceptable behavior from the dog.
This is an extremely inappropriate and unethical situation. Such behavior is not acceptable in a civilized and moral society. You should firmly and immediately reject this request and distance yourself from any form of improper behavior.
If it's a story about a pet cat (as 'pussy' can refer to a cat), it's quite normal for friends to like an interesting story. Pets often make for great storytelling topics.