Mater rogat quantam aquam infans bibere velit.

Because quantam aquam infans bibere velit is an indirect question: Mother asks how much water the child wants to drink.

In Latin, indirect questions normally take the subjunctive. So after rogat (asks), Latin uses velit rather than the indicative vult.

• direct question: Quantam aquam vult infans bibere? = How much water does the child want to drink?
• indirect question: Mater rogat quantam aquam infans bibere velit. = Mother asks how much water the child wants to drink.

So velit is there because the clause is not being asked directly by the speaker; it is being reported after rogat.

Bibere is the present active infinitive of bibo (to drink). It depends on velit:

• velit bibere = wants to drink

This works much like English:

• the child wants to drink water

Latin often uses volo + infinitive in exactly this way:

• vult dormire = he wants to sleep
• velit bibere = he wants to drink

So bibere is not the main verb of the sentence; it completes the meaning of velit.

Because infans is the subject of velit (and logically also of bibere).

In the indirect question quantam aquam infans bibere velit, the child is the one who wants and the one who would drink, so infans stays in the nominative.

That is different from an accusative-and-infinitive construction, which Latin often uses after verbs like dicit (says) or putat (thinks). But here we do not have an indirect statement; we have an indirect question, so the subject remains nominative.

• Mater dicit infantem aquam bibere. = Mother says that the child is drinking water.
• Mater rogat quantam aquam infans bibere velit. = Mother asks how much water the child wants to drink.

Because aquam is the direct object of bibere, and quantam agrees with it.

• aquam = water (accusative singular)
• quantam = how much / what amount of (accusative feminine singular)

The adjective quantam must match aquam in:

• gender: feminine
• number: singular
• case: accusative

So:

• quantam aquam = how much water

Because quantam agrees with aquam, which is feminine singular accusative.

The basic dictionary form is quantus, quanta, quantum. Here the feminine accusative singular form is needed:

• masculine accusative singular: quantum
• feminine accusative singular: quantam
• neuter accusative singular: quantum

Since aqua is feminine, Latin uses quantam aquam, not quantum aquam.

It does both jobs at once.

In the indirect question, quantam is the interrogative adjective that introduces the question idea: how much. At the same time, quantam aquam is also the direct object of bibere.

So in one phrase Latin expresses:

• the thing being asked about: how much
• the thing being drunk: water

That is why the clause can be understood as:

• how much water the child wants to drink

The main verb is rogat.

Sentence structure:

• Mater = subject of the main clause
• rogat = main verb
• quantam aquam infans bibere velit = subordinate clause (an indirect question)

So the sentence is built like this:

• Mater rogat = Mother asks
• quantam aquam infans bibere velit = how much water the child wants to drink

Even though velit is a finite verb too, it belongs to the subordinate clause, not the main clause.

Yes. Latin word order is fairly flexible because the endings show the grammatical roles.

This sentence could be rearranged in several ways without changing the basic meaning, for example:

• Mater quantam aquam infans bibere velit rogat.
• Quantam aquam infans bibere velit mater rogat.
• Infans quantam aquam bibere velit mater rogat.

However, the original order is quite natural:

• main clause first: Mater rogat
• then the indirect question: quantam aquam infans bibere velit

Latin word order often helps with emphasis or style, not just grammar.

Yes. After a main verb in a primary tense like rogat (present), Latin normally uses the present subjunctive in an indirect question when the action is viewed as present or future relative to the main verb.

So:

• rogat = she asks
• velit = wants / may want at the same time as the asking

If the main verb were in a past tense, Latin would often use the imperfect subjunctive instead:

• Mater rogabat quantam aquam infans bibere vellet.
• Mother was asking how much water the child wanted to drink.

So velit fits the normal sequence after a present main verb.

The one doing the drinking is infans.

Even though bibere is an infinitive and does not show person or number by itself, its subject is understood from the clause:

• infans bibere velit = the child wants to drink

So the child is both:

• the subject of velit
• the understood subject of bibere

Latin can express how much water in more than one way, and learners may indeed meet other patterns. In this sentence, though, quantam aquam is a straightforward and perfectly understandable way to say how much water, with quantam agreeing directly with aquam.

So for this sentence, the important thing to notice is simply:

• quantam modifies aquam
• both are accusative because they function together as the object of bibere

If you later see different ways of expressing quantity, that is a broader style and usage question, not a problem with this sentence itself.

Here rogat means simply asks in the sense of asks the question.

The sentence does not state whom the mother is asking; it only tells us what she asks:

• how much water the child wants to drink

If Latin wanted to specify the person being asked, it could add that separately. But in this sentence the focus is on the content of the question, not the person addressed.