Magistra dicit bonam pronuntiationem discipulis magno auxilio esse.

The sentence has two parts:

• Magistra dicit = The teacher says
• bonam pronuntiationem discipulis magno auxilio esse = the statement being reported

Latin often reports what someone says by using an indirect statement construction:

• a subject in the accusative
• a verb in the infinitive

So here the teacher is saying good pronunciation to be a great help to the students.

Because Latin usually does not use a separate word like English that after verbs of saying, thinking, knowing, and perceiving.

Instead, it uses the accusative-and-infinitive construction:

• English: The teacher says that good pronunciation is...
• Latin: Magistra dicit bonam pronuntiationem ... esse

So the idea of that is built into the grammar rather than expressed by a separate word.

Because it is the subject of the indirect statement.

In English, the subject of the reported clause stays nominative:

• good pronunciation is...

But in Latin indirect statement, the subject changes into the accusative:

• direct statement: bona pronuntiatio ... est
• indirect statement: bonam pronuntiationem ... esse

So bonam pronuntiationem means good pronunciation, but grammatically it is accusative because it depends on dicit.

Because in an indirect statement, Latin uses an infinitive rather than a finite verb.

So:

• direct statement: bona pronuntiatio discipulis magno auxilio est
• indirect statement after dicit: bonam pronuntiationem discipulis magno auxilio esse

English uses that ... is. Latin uses accusative + infinitive, so est becomes esse.

Magistra is nominative singular.

It is the subject of dicit, so it tells us who is doing the saying:

• magistra = the teacher
• dicit = says

So Magistra dicit means The teacher says.

Discipulis is dative plural of discipulus.

It means for the students or to the students in the sense of with reference to them / for their benefit.

So it tells us who is affected by the help:

• discipulis = for the students
• good pronunciation is a great help to the students

Magno auxilio is a very common Latin pattern. It is a dative of purpose and means something like:

• for a great help
• more naturally in English: a great help

Together with discipulis, it forms the double dative construction:

• discipulis = dative of reference/advantage (for the students)
• magno auxilio = dative of purpose (for a great help)

So literally the Latin says something like:

• good pronunciation to be for a great help to the students

More natural English:

• good pronunciation is a great help to the students

The form auxilio could look either dative or ablative, because those forms are identical here. But in this sentence it is understood as dative, not ablative.

Why?

Because with esse and another dative like discipulis, Latin commonly uses the double dative construction:

• discipulis magno auxilio esse

That strongly points to:

• discipulis = for the students
• magno auxilio = for a great help

So this is not mainly an ablative idea like by means of help. It is the dative construction to be a help to someone.

Because magno agrees with auxilio, not with pronuntiationem.

• auxilium is neuter singular
• in the dative singular, that becomes auxilio
• the adjective magnus must match it, so we get magno

So:

• magno auxilio = for a great help
• not magna auxilio, because that would not agree with auxilio

Because the adjective agrees with the noun in gender, number, and case.

Here:

• pronuntiationem = feminine singular accusative
• bonam = feminine singular accusative

So bonam pronuntiationem means good pronunciation.

This is especially important in Latin because word order is flexible. Even if the words were separated, their matching endings would still show that they belong together.

The direct statement would be:

Bona pronuntiatio discipulis magno auxilio est.

That means:

• Good pronunciation is a great help to the students.

Then after dicit, Latin changes it into indirect statement:

• bona pronuntiatio → bonam pronuntiationem
• est → esse

So:

• direct: Bona pronuntiatio discipulis magno auxilio est.
• indirect: Magistra dicit bonam pronuntiationem discipulis magno auxilio esse.

No. Latin word order is much freer than English word order because the endings show the grammatical relationships.

This order is perfectly natural:

• Magistra dicit bonam pronuntiationem discipulis magno auxilio esse.

But Latin could rearrange the words for emphasis and still keep the same basic meaning, as long as the forms stay the same.

A few things are especially common, though:

• the main verb dicit often comes early
• the infinitive esse often comes at the end
• related words may be grouped together, but they do not have to be

So the order helps style and emphasis more than basic grammar.