Magistra discipulis narrat reum aequum iudicium sperare debere, non rumorem falsum timere.

The sentence has a simple main clause plus a reported statement.

Main clause:

• Magistra = the subject
• discipulis = the people she is telling
• narrat = the main verb

Reported statement:

• reum aequum iudicium sperare debere, non rumorem falsum timere

So the overall pattern is:

The teacher tells the students [that ...].

In Latin, that [that ...] part is expressed with an accusative-and-infinitive construction rather than a separate that-clause.

Because it is the indirect object: to the students.

With verbs like narrare in this kind of sentence, Latin often uses:

• a nominative subject
• a dative person being told
• then the content of what is told

So:

• Magistra = the teacher
• discipulis = to the students
• narrat = tells

This is very natural Latin.

In a normal main clause, yes, the subject would be nominative. But here reum is the subject of an infinitive inside an indirect statement.

Latin usually puts the subject of reported speech/thought in the accusative:

• reum = the defendant
• debere = to ought / to be supposed to / ought

So reum ... debere means that the defendant ought ...

This is one of the most important Latin constructions to learn:

• main verb of saying/thinking/perceiving
• accusative subject
• infinitive verb

So reum is not the direct object of narrat. It is the subject of the reported statement.

Yes. This is a classic accusative + infinitive indirect statement.

After narrat, instead of saying:

• that the defendant ought to hope ...

Latin says:

• reum ... debere

Literally, that is something like:

• the defendant to ought

Of course that is not good English, but it shows the structure.

Here:

• reum = accusative subject of the indirect statement
• debere = infinitive verb of the indirect statement

Then sperare and timere depend on debere.

Because the verb inside an indirect statement is usually an infinitive, not a finite verb.

If Latin used a direct statement, it could say something like:

• reus aequum iudicium sperare debet = the defendant ought to hope for a fair trial

But after narrat, Latin changes the reported statement into indirect statement:

• reum aequum iudicium sperare debere

So:

• debet = finite verb in a normal clause
• debere = infinitive in indirect statement

Reum is the understood subject of both actions.

So the defendant is the one who:

• sperare = hopes
• timere = fears

Latin does not need to repeat the subject. Once reum has been introduced as the subject of the indirect statement, it naturally carries over through the rest of that reported content.

Yes, that is the most natural way to understand it.

The sense is:

• the defendant ought to hope for a fair trial
• and not fear a false rumor

Latin often leaves out a repeated word when it is easy to understand. So you can mentally expand it as:

• reum aequum iudicium sperare debere, non rumorem falsum timere debere

But Latin does not need to repeat debere.

Because they are the direct objects of the infinitives:

• aequum iudicium sperare = to hope for a fair trial
• rumorem falsum timere = to fear a false rumor

Each phrase has:

• an infinitive verb
• its own direct object in the accusative

So:

• aequum iudicium goes with sperare
• rumorem falsum goes with timere

Also notice adjective agreement:

• aequum agrees with iudicium
• falsum agrees with rumorem

It negates the second infinitive phrase: rumorem falsum timere.

So the contrast is:

• sperare
• non ... timere

In other words:

• the defendant ought to hope for a fair trial,
• not fear a false rumor.

It does not negate narrat. The sentence does not mean the teacher does not tell the students ...

Because Latin word order is much freer than English word order. Endings show grammatical function, so Latin can move words around for emphasis, balance, or style.

Here the order helps group ideas:

• Magistra discipulis narrat
  first gives the main clause

• reum
  introduces the subject of the reported statement early

• aequum iudicium sperare debere
  gives the first idea

• non rumorem falsum timere
  gives the contrasting second idea

The comma also helps show that contrast:

• hope for a fair trial,
• not fear a false rumor

So the order is not random; it is flexible but meaningful.

A very literal translation would be:

The teacher tells the students the defendant to ought to hope for a fair trial, not to fear a false rumor.

That is awkward English, but it mirrors the Latin structure.

A better natural English translation is:

The teacher tells the students that the defendant ought to hope for a fair trial, not fear a false rumor.

So the literal version helps you see the grammar, while the natural version gives good English.