Ben here. I want to say that I think there is a problem with having 2 different english definitions for this sentence in Vietnamese. When using the definite article "the" here in the sentence "I drink the water" has a very different meaning to "I drink water". With the use of the definite article, it implies that the speaker is talking about the drinking water from the tap or another source of water such as a spring. In Vietnamese, you would need to use different words such as "Tôi uống nước từ vòi nước" = I drink the "tap" water" or "I drink water from the tap". to express that meaning. So the problem is that it is not accurate to say that this Vietnamese sentence can have both these translations in English because they are do not equal the same in Vietnamese. Does anyone agree?
Yep, I agree. "I drink water" -> Tôi uống nước (We don't really know or care about the source of that kind of water). However, "I drink the water" -> Tôi uống (thứ/loại) nước này/đó/ấy/từ nguồn nào đó etc (We already know the source of that kind of water).
Please never try to force foreign grammar structure into Vietnamese because we may accidentally/indirectly lose its original precise and concise structure. For examples:
I drink water from the river/Tôi uống nước sông (no need to add from/từ)
I pick up the cigarette and smoke it/Tôi cầm điếu thuốc lên và hút (no need to add it/nó)
She love her children very much/Bà ta rất thương con (no need to add her/của bà ta). Also she means "cô ta/bà ta" but we should say "bà" to address a female with child(ren).
I don't agree with what you wrote:
I drink water from the river/Tôi uống nước sông (no need to add from/từ). -> Is there anything wrong with "Tôi uống nước TỪ sông" or, to be more exact, "Tôi uống nước TỪ con sông"? Why is there no need to add TỪ?
I pick up the cigarette and smoke it/Tôi cầm điếu thuốc lên và hút (no need to add it/nó) -> What's wrong with "Tôi cầm điếu thuốc lên và hút NÓ"? Why is there no need to add NÓ?
She loves her children very much/Bà ta rất thương con (no need to add her/của bà ta) -> Again, what's wrong with "Bà ta rất thương con CỦA BÀ TA"? How about "Bà ta rất thương con CỦA BÀ" and "Bà ta rất thương con CỦA MÌNH"?
Just because a sentence sounds unnatural to you doesn't mean it's not grammatically correct.
Please also keep in mind that this is the VERY BEGINNING of the Vietnamese course for FOREIGN LEARNERS where they can only translate word by word. You'll likely confuse learners more by omitting words.