Puer aqua caret.

Because puer is in the nominative singular, which is the case normally used for the subject of a Latin sentence.

• puer = boy
• nominative singular of puer, puerī

So puer is the one doing or experiencing the action/state expressed by the verb.

Because caret comes from careō, and careō takes the ablative, not the accusative.

So:

• aquā = with water lacking / without water / of water
• not aquam, because this verb does not take a direct object in the accusative

This is one of the important things to memorize with careō:

• careō + ablative = to lack, to be without

In texts without macrons, aquā is often written simply as aqua, so the form can look identical to the nominative.

Because for many first-declension nouns, the nominative singular and ablative singular look the same when macrons are not written.

For aqua:

• nominative singular: aqua
• ablative singular: aquā

The difference is the long final -ā, but many beginner texts leave macrons out, so both appear as aqua in ordinary spelling.

You can tell it is ablative here because careō requires the ablative.

Caret is:

• third person singular
• present tense
• active voice
• indicative mood

from the verb careō, carēre, caruī, caritūrus.

So caret means he/she/it lacks or is without.

Because the subject is puer, the sentence means the boy lacks... or the boy is without...

Because careō is a second-conjugation verb. Second-conjugation verbs have -ēre in the infinitive and usually form the present tense like this:

• careō = I lack
• carēs = you lack
• caret = he/she/it lacks
• carēmus = we lack
• carētis = you all lack
• carent = they lack

So caret is the correct third-person singular form.

No. Classical Latin does not have a definite article like English the or an indefinite article like English a/an.

So puer can mean:

• the boy
• a boy

and aqua can mean:

• water
• the water

You decide from context how to translate it most naturally.

Yes. Latin word order is more flexible than English because the endings show the grammatical relationships.

So all of these could mean essentially the same thing:

• Puer aquā caret.
• Aquā puer caret.
• Caret puer aquā.

However, the word order may slightly change the emphasis.

• Puer aquā caret is a straightforward, neutral order.
• Aquā puer caret puts more attention on water.
• Caret puer aquā may sound more literary or marked.

Either can work. English uses different natural expressions depending on context.

For Puer aquā caret, possible translations include:

• The boy lacks water.
• The boy is without water.
• The boy has no water.

Grammatically, careō means to lack or to be without, and it governs the ablative.

The dictionary form is:

• puer, puerī = boy

It is a second-declension masculine noun.

Some of its forms are:

• nominative singular: puer
• genitive singular: puerī
• accusative singular: puerum
• ablative singular: puerō

A learner often notices that puer keeps the -e- in the nominative singular, unlike some other second-declension nouns.

The dictionary form is:

• aqua, aquae = water

It is a first-declension feminine noun.

Relevant forms here are:

• nominative singular: aqua
• genitive singular: aquae
• accusative singular: aquam
• ablative singular: aquā

In this sentence, the form is ablative singular because of careō.

By itself, the present indicative can mean either, depending on context.

So Puer aquā caret could mean:

• The boy lacks water right now
• The boy is without water as a general situation

Latin does not always make that distinction explicit. Context tells you how specific or general the statement is.