Other nations "territorial waters?"

For fucks sake. Let's go through things piece by piece, remembering that China and Taiwan have completely aligned claims by policy.

The Paracels are within 200nm and outside 12nm of both China and Vietnam (and, for what it's worth, were granted to China by North Vietnam prior to the Vietnam War and that China kicked the South Vietnamese from the islands after they occupied them during the Vietnam War).

The Spratlys are disputed between China/Taiwan, the Philippines, Malaysia, Vietnam, and Brunei. These islands are in no country's territorial waters, which is the entire reason for the dispute in the first place: a successful claim to these islands significantly expands a country's EEZ and territorial waters in the region. Both Vietnam and China/Taiwan make claims in the area based on historical precedent, while the Philippines, Brunei, and Malaysia make claims based on their EEZ extending to those islands, and those islands must thus also be part of their EEZ (and, since they're clearly territory, expand their EEZ further). Again, these islands are in nobody's territorial waters, which is the entire point of the debate.

Scarborough Shoal is about 198km from the nearest point in the Philippines and, again, does not fall within Filipino territorial waters.

Given that we've established that these islands are not in a country's territorial waters, let's take a closer look at what can be claimed based on the lawful methods for acquisition of sovereignty: effective occupation, cession, prescription, conquest, and accretion.

These basically involve projecting ownership over an island (e.g. by building outposts on it, or conquering it, or otherwise making the island their removed). You can feel free to extrapolate these conditions onto each of the above cases, but you'll find that the Chinese claims are rather strong given these lawful methods for acquisition of sovereignty. They are not absolute, which is why there's still dispute, but it's not like their claims are entirely unreasonable under international law (even if the obsession with the nine-dash line rather than other mechanisms for actually gaining sovereignty is probably harming their case). Most notably, the Paracels should fall very clearly under either effective occupation or conquest and I'm really not sure why Vietnam is so adamantly protesting this issue given that their claim is so weak.