La preside controlla il registro, mentre la supplente prepara l’interrogazione.

Here they refer to female people, so the article is la.

Both preside and supplente can be common-gender nouns, meaning the noun form may stay the same while the article shows whether the person is male or female:

• il preside = a male principal
• la preside = a female principal
• il supplente = a male substitute teacher
• la supplente = a female substitute teacher

So in this sentence, the article tells you both people are female.

Because interrogazione is a feminine singular noun that begins with a vowel.

In Italian, la becomes l’ before a vowel:

• la scuola
• l’interrogazione
• l’amica

So la interrogazione is not the normal form here; l’interrogazione is.

They are both present indicative, third person singular forms:

• controlla = he/she checks
• prepara = he/she prepares

They match the singular subjects:

• la preside controlla
• la supplente prepara

The infinitive forms would be controllare and preparare, but after a subject you normally need a conjugated verb, not the infinitive.

Mentre usually means while or whereas.

In this sentence, it most naturally means while, because the two actions are happening at the same time:

• La preside controlla il registro, mentre la supplente prepara l’interrogazione.

It can also sometimes introduce contrast, more like whereas, depending on context.

Because registro begins with a normal consonant sound, r.

For masculine singular nouns, Italian usually uses:

• il before most consonants
• lo before certain special sounds, such as z, s + consonant, gn, ps, pn, x, y

So:

• il registro
• il libro
• but lo studente
• lo zaino

Since registro starts with r, the correct article is il.

Not exactly.

In school Italian, interrogazione usually means an oral test, oral questioning, or a situation where a teacher calls on a student to answer questions aloud.

So here it does not sound like a police-style interrogation. It is a normal school term.

Italian uses definite articles more often than English.

In this sentence, the article shows that the speaker is talking about specific, identifiable people and things in a school context:

• la preside = the principal
• la supplente = the substitute teacher
• il registro = the register / class record book

English may sometimes sound more flexible about articles in similar contexts, but Italian generally wants them here.

Yes. Italian word order is more flexible than English.

For example, you could also say:

Mentre la supplente prepara l’interrogazione, la preside controlla il registro.

That means essentially the same thing. The original version is just a very natural, neutral order.

Because Italian usually does not need them.

The verb ending already tells you the person and number, and in this sentence the subjects are stated explicitly anyway:

• la preside controlla
• la supplente prepara

Adding lei would usually be unnecessary unless you wanted extra emphasis or contrast.

Not necessarily.

In a school context, registro can refer to:

• a class register
• an attendance record
• a gradebook
• even an electronic register in modern schools

So the sentence does not force the idea of a paper book, even though that is one possible image.

The comma separates the two clauses:

• La preside controlla il registro
• mentre la supplente prepara l’interrogazione

In Italian, a comma before mentre is very common when two full clauses are being linked, especially when they have different subjects. It helps readability and makes the structure clearer.

Yes.

Mentre can express:

1. simultaneous time
   
   • while
2. contrast
   
   • whereas

In this sentence, the most natural reading is the time meaning: both actions are going on at once. But grammatically, mentre is a word that can also introduce contrast in other contexts.