Quantum ad valetudinem suam, puer melius valet.

Quantum ad is an idiomatic expression meaning as for, with regard to, or as far as ... is concerned.

So:

• Quantum ad valetudinem suam = as far as his health is concerned
• more literally: as much as concerns his health

It introduces the topic or respect in which the rest of the sentence is true.

Because ad normally takes the accusative, and in the expression quantum ad + accusative, the noun after ad stays in the accusative.

So:

• valetudo, valetudinis = health
• accusative singular = valetudinem

This whole phrase functions like with regard to his health.

Here quantum is the neuter accusative singular form of quantus, but it is being used in a somewhat fixed idiomatic way with ad.

You do not need to translate it word-for-word as an ordinary adjective. In this phrase, quantum ad works together as a unit meaning:

• as to
• with respect to
• as far as ... is concerned

So although quantum originally comes from a word meaning how much, here the phrase should be learned as an idiom.

Because suus, sua, suum is the reflexive possessive adjective. It refers back to the subject of the clause.

In this sentence, the subject is puer (the boy), so:

• valetudinem suam = his own health / the boy's health

If Latin used eius, that would usually refer to someone else's health, not the boy's own.

So suam is exactly what you would expect here.

Valet is from valeo, which basically means to be strong, to be well, or to be in good health.

Depending on context, it can mean:

• is well
• is healthy
• has strength
• sometimes more generally, is strong or has power

In this sentence, because the topic is health (valetudo), valet clearly means something like is doing well health-wise or is in good health.

Because melius is the comparative adverb meaning better, while melior is the comparative adjective meaning better.

Here melius modifies the verb valet:

• puer melius valet = the boy is better / the boy is doing better

Compare:

• bonus puer = a good boy
• melior puer = a better boy ← adjective modifying a noun
• puer melius valet = the boy is better ← adverb modifying a verb

So melius is correct because it describes how he is well.

Yes. Puer is nominative singular, so it is the subject:

• puer = the boy

The main clause is:

• puer melius valet = the boy is better

The opening phrase quantum ad valetudinem suam is not the subject; it just sets the topic: as for his health.

Yes, Latin word order is flexible. This sentence starts with the topic phrase:

• Quantum ad valetudinem suam = as for his health

Then comes the main statement:

• puer melius valet = the boy is better

This order is natural because it frames the statement first: with regard to his health...

Latin could rearrange things for emphasis, for example:

• Puer, quantum ad valetudinem suam, melius valet.
• Puer melius valet, quantum ad valetudinem suam.

But the given order is a very normal way to foreground the respect in which the statement is true.

The comma reflects a pause in English-style punctuation and helps show that the opening phrase is a kind of introductory topic:

• Quantum ad valetudinem suam, = As for his health,

Ancient Latin manuscripts did not use punctuation the way modern editions do, so the comma is mainly an editorial aid for readers.

It helps you see the structure:

1. introductory phrase
2. main clause

Yes. Literally it means:

• his health

More exactly:

• valetudinem = health (accusative singular)
• suam = his own

So the phrase is literally his own health, though in natural English we usually just say his health.

Yes, especially when talking about health. Latin often uses valere for being well or recovering.

So:

• valet = he is well
• melius valet = he is better
• optime valet = he is very well

This is a very natural Latin pattern.

To an English speaker it may feel a little repetitive, but in Latin it is perfectly normal.

The first part:

• quantum ad valetudinem suam = as regards his health

sets the respect or topic.

The second part:

• melius valet = he is better / healthier

makes the actual statement.

So the sentence means something like:

• As far as his health goes, the boy is better.

The repetition is not clumsy in Latin; it is a clear and idiomatic way to express the idea.

Yes. Latin has several expressions for with regard to or as to, for example:

• de valetudine sua = about his health
• quod ad valetudinem suam attinet = as far as his health is concerned
• quantum ad valetudinem suam = as for his health

The form in your sentence is a compact and idiomatic one. It is worth learning as a set phrase.