'uống nước' sounds very sparse. The two words sound like one word altogether. Is the 'c' in 'nước' not pronounced?
According to the Wikipedia article on Vietnamese phonology, when a word ends with a "k" sound or "ng" sound, it should be pronounced with your lips closing at the end of the sound, almost cutting it off abruptly. It's similar to how the 't' in "cat" isn't pronounced completely.
So nước, transliterated into English orthography, would sound something like noo-uh-km, where 'm' represents the mouth closing at the end of the syllable.
No, we don't always close our lips at the end of the word when we pronounce words with -c or -ng endings. In fact, we only close our lips when pronounce words with -oc, -ôc, -uc, -ong, -ông, and -ung endings. For example: học, ốc, cục, õng, bổng, sùng.
I'll try to explain more rules in the next levels when possible.
Because we don't pronounce the very last consonants of a word as they should be in English. For example: "nước" is pronounced as /'nʊək/ without the /kə.../ sound at the end of it.
Try saying /nʊək/ then stop immediately when you reach the end of the word. Don't make the extra /kə.../ sound which is like you are gargling or clearing your throat. The same rule applies to most of the last consonants of any other words. This makes "uống nước" sound like "uốnước" /'uon'ʊək/ without the /kə.../ sound at the end of it.