"Which desk is it?"
Theres nothing modifying it. です isnt a real verb and どの doesnt need a particle like この and その.
You're attributing "which" to the desk. You're not so much asking "which desk is it", you're asking "out of these desks, which one is it". It is not explicitly faulty, but it is remarkably clumsy.
どれ entirely takes the place of the noun. You can't use どれ + noun. If you want to use a demonstrative ("which" in this case) and the noun both, you have to use どの.
It's the same with あの vs. あれ, その vs. それ, etc. The -の words are used when you're still mentioning the noun, while the -れ words entirely replace the noun.
Technically that is correct, assuming there's "many" desks, but it could be just 2, in which cases that'd be incorrect.
It's not the particle de, it's desu. It's more clear when it's kanji. [どの][つくえ][です][か] = [which][desk][is it][?]