Non timeo ne Lucia erret, quia semper animo attento magistram audit.

After verbs of fearing, Latin uses a special construction:

• timeo ne ... = I fear that ...
• timeo ut ... = I fear that ... not / I am afraid that ... may not

So here ne is part of the standard fear-clause pattern. It does not have its usual straightforward negative force.

This is why timeo ne Lucia erret means I fear that Lucia may go wrong / make a mistake, not I fear that Lucia may not go wrong.

No.

• non negates the main verb timeo
• ne belongs to the fear construction

So:

• timeo ne Lucia erret = I fear that Lucia may go wrong
• non timeo ne Lucia erret = I do not fear that Lucia may go wrong

The non changes the meaning of timeo, not the meaning of ne.

Because fear clauses normally take the subjunctive in Latin.

So after timeo ne, the verb in the subordinate clause is expected to be subjunctive:

• erret = present subjunctive, 3rd person singular

This is not mainly about uncertainty in the English sense. It is simply the normal grammar of this type of clause.

In this sentence, the present subjunctive fits the idea of something viewed as possible or future relative to timeo.

Erret is:

• present
• subjunctive
• active
• 3rd person singular

It comes from erro, errare.

So the base idea is she may err / go astray / make a mistake, depending on context.

No, because this is a full subordinate clause introduced by ne, not an accusative-and-infinitive construction.

In the clause ne Lucia erret, Lucia is the subject of the finite verb erret, so it stays in the nominative.

A learner may expect an accusative because Latin often uses accusative subjects in indirect statement, but this is not indirect statement. It is a fear clause.

Because audio takes a direct object in the accusative.

So Latin says:

• magistram audit = she hears / listens to the teacher

English usually says listen to the teacher, with to, but Latin does not need a preposition here.

So magistram is accusative singular, the direct object of audit.

Animo attento is an ablative phrase meaning something like:

• with an attentive mind
• more naturally, attentively

It describes the manner in which Lucia listens.

So the sense is that she listens to the teacher in an attentive way.

This is a common Latin pattern.

With an ablative of manner, Latin often uses cum if there is just a noun:

• cum cura = with care

But if the noun has an adjective, Latin often omits cum:

• magna cura
• animo attento

So animo attento is perfectly normal Latin for with an attentive mind.

Because quia here introduces a normal statement of real cause:

• quia ... audit = because she listens ...

When Latin presents the reason as a fact, it usually uses the indicative.

So:

• audit = present indicative, 3rd person singular

A subjunctive after quia is possible in some special contexts, but not in this straightforward sentence.

Latin often leaves subject pronouns unstated because the verb ending already shows the person and number.

• audit = he/she/it listens

Since no new subject is introduced in the quia clause, the natural understanding is that the subject is still Lucia.

So:

• Lucia erret = Lucia may err
• quia ... audit = because she listens

Yes, Latin word order is much more flexible than English word order.

This sentence is arranged quite naturally:

• Non timeo first gives the main point right away
• ne Lucia erret gives the thing not feared
• quia semper animo attento magistram audit adds the reason

Within the reason clause, Latin places:

• semper near the idea it modifies
• animo attento before the verb to show manner
• audit at the end, which is very common in Latin prose

Other orders would be possible, but they would slightly change emphasis rather than basic meaning.