Tôi dùng bình tưới để tưới cây.

Because the two tưới words are doing different jobs.

• In bình tưới, tưới helps name the object: a watering can / watering container / sprayer.
• In tưới cây, tưới is the main verb to water.

This kind of repetition is very normal in Vietnamese. A very literal breakdown is:

• Tôi = I
• dùng = use
• bình tưới = watering can / watering container
• để = to / in order to
• tưới cây = water plants

So the sentence is structurally very natural, even if English would usually avoid repeating water.

Here, để means to, in order to, or for the purpose of.

So:

• dùng bình tưới để tưới cây = use a watering can to water plants

A very common Vietnamese pattern is:

• dùng + thing + để + do something

Examples:

• Tôi dùng dao để cắt bánh. = I use a knife to cut the cake.
• Cô ấy dùng điện thoại để gọi mẹ. = She uses a phone to call her mother.

So in your sentence, để connects the tool with its purpose.

It is best understood as a noun phrase / compound noun.

• bình = container, bottle, can, tank
• tưới = water, sprinkle

Together, bình tưới means something like watering container. Depending on context, it could refer to:

• a watering can
• a sprayer
• sometimes another container used for watering

Vietnamese often builds object names this way: a general noun plus a word showing function.

Yes. Tôi dùng bình tưới để tưới cây is correct, but many speakers would also say:

• Tôi tưới cây bằng bình tưới.

That means essentially the same thing: I water the plants with a watering can.

The difference is mainly in focus:

• dùng ... để ... emphasizes using something to do something
• bằng ... emphasizes the means/tool used

So both are fine:

• Tôi dùng bình tưới để tưới cây.
• Tôi tưới cây bằng bình tưới.

The second one may sound a little more natural in everyday speech because it avoids repeating tưới.

Both can mean use, but they are different in tone.

• dùng = common, everyday, conversational
• sử dụng = more formal, more written, more official

So in daily speech, dùng is usually the better choice here.

You could say:

• Tôi dùng bình tưới để tưới cây.
  This sounds natural.

You could also say:

• Tôi sử dụng bình tưới để tưới cây.
  This is grammatically correct, but it sounds more formal than most people would use in casual conversation.

Vietnamese usually does not require articles like a, an, or the.

So:

• bình tưới can mean a watering can, the watering can, or just watering can(s) depending on context.
• cây can mean plants, the plant, trees, or the plants, again depending on context.

If you want to be more specific, you can add words:

• một cái bình tưới = a watering can
• cái bình tưới đó = that watering can
• các cây = the plants / plants in plural
• mấy cây = a few plants

Vietnamese often leaves this information to context unless it needs to be made explicit.

It can mean both in different contexts, but in tưới cây, it often means plants in a general sense.

So depending on the situation, tưới cây might mean:

• water the plants
• water the tree(s)
• water the garden plants

In everyday Vietnamese, cây is often used broadly for living plants, not only large trees.

Sometimes, yes.

• Tôi dùng bình tưới để tưới cây. = full sentence, clear and neutral
• Dùng bình tưới để tưới cây. = possible if the subject is already understood, or if it is an instruction/note

Vietnamese often drops the subject when it is obvious from context. But if you are just learning, keeping tôi is a good habit because it makes the sentence complete and clear.

The word order is:

• Tôi = subject
• dùng = verb
• bình tưới = object
• để = purpose marker
• tưới cây = purpose/action

So the structure is:

• Subject + use + tool + để + action

A literal English-style gloss would be:

• I use watering-can to water plants.

This is a very useful Vietnamese pattern, and you can reuse it easily with other verbs.

Not here.

In Vietnamese, classifiers like cái are often used when:

• counting things
• pointing to a specific item
• emphasizing a noun in some contexts

So you might say:

• một cái bình tưới = one watering can
• cái bình tưới này = this watering can

But after dùng, it is very normal to say just:

• dùng bình tưới

without a classifier.

So your sentence is perfectly natural as written.

A rough pronunciation guide is:

• Tôi ≈ toy
• dùng ≈ zoong / yoong depending on accent
• bình ≈ binh
• tưới ≈ too-ee with a rising tone
• để ≈ deh with a dipping tone
• cây ≈ gay / kuyeh-like, depending on how carefully you pronounce it

The tones are important:

• tôi: level tone
• dùng: low falling tone
• bình: low falling tone
• tưới: rising tone
• để: hỏi tone
• cây: level tone

If you want to sound natural, one especially useful thing is to practice the rhythm in chunks:

• Tôi dùng bình tưới / để tưới cây

Not really awkward, but it is slightly more explicit than everyday speech often needs.

Vietnamese allows this kind of repetition very easily:

• bình tưới = watering can
• tưới cây = water plants

So the sentence is correct and understandable. Still, many speakers might prefer a smoother version such as:

• Tôi tưới cây bằng bình tưới.

That said, your original sentence is a very good example of the grammar pattern dùng X để làm Y, so it is especially useful for learners.