Zander said:
While the dwarves (or dwarfs) in the Grimm story are about the size of a seven-year-old and do live in a cottage in the woods, they are good, very orderly (lawful?) and work in the mountains looking for precious metals all of which suggests beings that approximate D&D dwarves more than gnomes or elves. Moreover, in other tales, the Grimm brothers have small but mischievous creatures called elves, so at least as far as the Grimm brothers are concerned Dwarf ≠ Elf.
Actually, this illustrates the problem of your last question to me nicely, and it's more or less the answer. The Grimm brothers are familiar with elves, because one of their publications was the collection "Irische Elfenmärchen" (Irish Fairy Tales, 1826). The literal translation would be "Irish elf fairy tales", if you take "fairy tales" as a set expression. The word "elf" is not really used much in German, except when stories from other countries are told. In German, dwarf, gnome, hobgoblin (kobold) or 100 other expressions are used for the exact same concept: a mostly small magical being living below the earth or in a mountain, which also describes the Irish elf concept perfectly. Also, the typical English versions, like brownies, are covered within this range.
Add to this that, in Germanic tradition, smithing is inherently magical, and you will see why dwarves are considered magical. That's also the reason why Alberich is considered magical. In translations from German to English, the German words for "small magical being", whatever this may be (they all mean basically the same and are used interchangeably), are then often replaced by the word "elf".
This book, "Irish Fairy Tales", deals in detail with the naming of the little people. The Grimm brothers pointed out that they only used the non-German word "elf" in their stories, because this had been introduced with popular stories from England at the end of the 18th century. Then they explain the German version "alb" or old Nordic "alfr" as just meaning "ghost", take the Nibelung Alberich as prime example for an elf and point to the fact that even in the Edda (they don't say which one), one of the dwarves had the name "alfr".
They explain the differences between light elves and dark elves in the Nordic mythology, but then take the dwarf Alberich as a prime example of a mixture of both elven concepts. This shows that you are definitely wrong with your opinion of the treatment of dwarves and elves by the Grimm brothers. They saw the terms as interchangeable.