The term "gnome" was first used by the medieval writer Paracelcus, who used the word to name earth elementals; and he called the air, water, and fire elementals sylphs, undines, and salamanders, respectively. Over time, gnomes came to be synonymous with goblins, kobolds, knockers, spriggans, and other diminutive subterranean fairies of dubious morality. Not to be confused, of course, with the elf/dwarf/troll sort of fairy, which came out of Norse myth and somehow managed to become many different fairies, yet further confused with gnomes, sprites, and everything else. Tracing the origins of mythical creatures is basically a boggled mess (boggles... I forgot boggles, which are also bogarts and brownies, the gnomes or goblins of Sottish and English myth... darn).
And yes, Tolkien called his Noldori Elves "Gnomes" every once and a while, so while the "David the Gnome" type never did exist in Middle-Earth, there was something called a gnome. And yes, vampires and werewolves are mentioned in Middle-Earth, but only rarely.... and as for mermaids, you'll have to read Tolkien's short story Roverandom.
And the Shannara books are good for reading just in case you run out of Valium.