Lucia dicit se a magistra interrogari non timere.

A helpful way to parse it is:

• Lucia = subject of the main verb
• dicit = main verb, says
• se ... non timere = the reported statement, literally herself not to fear
• a magistra interrogari = what she does not fear, to be questioned by the teacher

So the backbone is:

• main clause: Lucia dicit
• indirect statement: se non timere
• infinitive depending on timere: interrogari
• agent with the passive: a magistra

Because Latin often uses indirect statement instead of a that-clause after verbs like dicit.

In English, we say:

• Lucia says that she is not afraid

In Latin, after verbs of saying, thinking, knowing, hearing, and so on, the usual pattern is:

• accusative subject + infinitive

So instead of a separate word meaning that, Latin gives you:

• se non timere = that she is not afraid

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

Se is the reflexive pronoun, and it refers back to the subject of the main clause, here Lucia.

So:

• Lucia dicit se... = Lucia says that she...

Because the person in the reported statement is the same person as the subject of dicit, Latin uses se.

If the sentence meant that Lucia was talking about some other woman, Latin would use eam instead.

In a Latin indirect statement, the subject of the infinitive goes into the accusative case.

So even though se is logically the subject of timere, grammatically it appears in the accusative because of the indirect statement construction.

That is why you get:

• se timere = that she fears / is afraid

not nominative ea.

Because it is the verb of the indirect statement after dicit.

In direct speech, Lucia might say:

• non timeo = I am not afraid

But once that becomes reported speech after dicit, Latin changes the verb into an infinitive:

• Lucia dicit se non timere

So timere is not random here; it is exactly what Latin normally does in indirect statement.

Because it depends on timere.

The phrase is:

• interrogari timere = to fear to be questioned / to fear being questioned

So the structure is:

• se ... non timere = that she is not afraid
• interrogari = of being questioned

In smoother English, we usually say not to be afraid of being questioned, even though Latin uses the infinitive very naturally here.

Because Lucia is receiving the action, not doing it.

• interrogare = to question
• interrogari = to be questioned

Here the teacher is the one asking questions, and Lucia is the one being asked. So the passive is required by the meaning.

Because in Latin, the personal agent of a passive verb is usually expressed with:

• a or ab
  • ablative

So:

• a magistra = by the teacher

This goes naturally with the passive infinitive interrogari:

• interrogari a magistra = to be questioned by the teacher

Since magistra is a person, a/ab + ablative is the normal way to show who performs the action.

Non negates timere, not interrogari.

So the sense is:

• she says she is not afraid of being questioned

It does not mean:

• she says she is afraid of not being questioned

Latin word order is flexible, but here non timere clearly goes together.

Yes. In this kind of construction, se normally refers back to the subject of the governing verb, here Lucia.

So the sentence means that Lucia is speaking about herself.

If Latin wanted to say that Lucia says that another woman is not afraid, it would use something like eam, not se.

Both are present infinitives.

In indirect statement, the tense of the infinitive shows time relative to the main verb, not absolute time by itself.

So here:

• dicit = she says
• timere = to be afraid, at the same time as the saying
• interrogari = to be questioned / being questioned, also understood as contemporaneous

That is why English naturally translates the idea with present-time sense:

• she says that she is not afraid of being questioned

If Latin wanted to show action earlier than the saying, it would normally use a perfect infinitive instead.

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

For example, the same basic meaning could be arranged differently for emphasis, such as putting se earlier or dicit later.

Still, the order here is very natural:

• Lucia dicit first gives the frame
• then the reported statement follows
• non timere comes near the end as the core of what she says

So the order is not the only possible one, but it is a clear and ordinary one.