The “de” in the first sentence is necessary because “vos nouvelles” is actually indefinite in this sentence. We do not know which news are mentionned. So “de” acts as an undefined article.

(Your last sentence sounds a little bit strange as “eau” is uncountable… but is indeed more correct without “de”… to give another example, I would say “Où est ma bouteille d’eau?” Therefore, the water bottle is perfectly defined, so we don’t need “de”… However we could say “Nous avons besoin de bouteilles d’eau” with the undefined article again)

Hope I didn’t confuse you more! Any correction is appreciated 🙂

de is needed because vos is a an adjective before the noun nouvelles. Avoir de bonnes nouvelles, avoir de vos nouvelles… But if there’s no adjective, or it goes after the noun, you’d say avoir des nouvelles, avoir des voitures rouges…
If you say mon eau then there’s nothing to do with that because you won’t use the partitive, it’s your water and you want it all.

“de” must be added, because “vos nouvelles” would mean “all news about you“, meanwhile “de vos nouvelles” means “some news about you” (since “de” here represents “among”, or “from”).

It is the same use when you say : “Je mange de la viande”: “I eat meat” meanwhile “je mange la viande” would mean you eat the whole meat.