Is your cat licking behavior normal? We know a cat licks herself to keep clean. Licking fur also helps to smooth it, making it a better insulating layer. Licking fur also helps to keep your cat cool. The saliva evaporates cooling her down in the same way perspiration cools humans down (physics: latent heat of evaporation).
Your cat will lick her fur after you have handled her. This is to put her scent back on the spot where your scent has been left. She needs this to feel OK. A cat's world is a world of smells, ours is more visually orientated. She also licks off some of your scent to taste it (a form of communication). If she licks your hand she is tasting you, getting signals from you and grooming you as an act of friendship (as cats groom each other).
If a cat licks too much (abnormal cat licking behavior) it may be due to stress or ill health. Obviously a vet is required. One reason could be the food creating an allergic reaction. Dry cat food contains grain (frankly an unnatural ingredient for a cat), to which she may be allergic. Try wet cat food and different sorts or make your own cat food with supplements.
Perhaps the most likely reason for abnormal cat licking behavior is as displacement grooming. She is grooming to displace the feeling of stress she feels. We scratch our heads for the same reason. I happen to think that humans try too hard to make cats do what humans want or make her live like a human lives to the cat's detriment. More time should be spent ensuring that we create an environment for our cat that as near as possible meets her natural needs.
One cause of stress could be due to being confined, say, in an apartment. Cats normally like to roam a bit. I'll bet we'd be scratching our heads a hell of a lot if we were confined to an apartment 24/7. When we live with a human partner we consult the partner when we make decisions about living arrangements. A feline partner is no different. We can't consult with her. We can, though, understand her and give her what pleases her.
Drawing copyright and by Laurie treasures