Magistra narrat scutellas post cenam lotas esse et mortarium a puero nondum purgatum esse.

Because they are the subjects of an indirect statement after narrat.

Latin often uses this pattern after verbs of saying, thinking, knowing, hearing, and so on:

• verb of saying/thinking
• accusative subject
• infinitive

So here:

• Magistra narrat = The teacher says/tells
• scutellas ... lotas esse = that the bowls have been washed
• mortarium ... purgatum esse = that the mortar has not yet been cleaned

Even though scutellas and mortarium are logically the subjects of lotas esse and purgatum esse, Latin puts them in the accusative because of this construction.

Lotas esse is a perfect passive infinitive.

It is made from:

• a perfect passive participle: lotas
• plus esse

So:

• lavare = to wash
• lotus, -a, -um = washed
• lotas esse = to have been washed / to be washed in completed time relative to the main verb

In this sentence, it means that the washing is already completed by the time of the reporting.

Because the participle has to agree with the noun it goes with.

Scutellas is:

• accusative
• plural
• feminine

So the participle must also be:

• accusative
• plural
• feminine

That gives lotas.

Mortarium is:

• accusative
• singular
• neuter

So the participle must also be:

• accusative
• singular
• neuter

That gives purgatum.

This agreement is exactly like adjective agreement.

A puero means by the boy.

In a passive construction, Latin often uses:

• a/ab + ablative

to show the personal agent—the person who performs the action.

So:

• mortarium a puero purgatum esse = that the mortar has been cleaned by the boy

You use a/ab especially with people or other personal agents. Without a personal agent, Latin may simply use the ablative alone for means or instrument, but here the boy is an agent, so a puero is the normal form.

Post is a preposition that takes the accusative and means after.

So:

• post cenam = after dinner

Here cenam is accusative singular of cena.

This phrase tells you when the bowls were washed.

Nondum means not yet.

It modifies purgatum esse, so the idea is:

• mortarium a puero nondum purgatum esse
• that the mortar has not yet been cleaned by the boy

It shows that, at the time the teacher is speaking, the cleaning is still unfinished.

Because there are two coordinated indirect statements:

1. scutellas post cenam lotas esse
2. mortarium a puero nondum purgatum esse

Each one has its own infinitive phrase, so each can have its own esse.

Latin sometimes omits a repeated word when it is easy to understand, but here repeating esse makes the structure very clear.

Yes.

Magistra is nominative singular, so it is the subject:

• Magistra = the teacher
• narrat = tells / reports / says

So the basic frame is:

• The teacher reports that ... and that ...

A helpful way to divide it is:

• Magistra narrat
• scutellas post cenam lotas esse
• et
• mortarium a puero nondum purgatum esse

So the teacher reports two things:

1. that the bowls were washed after dinner
2. that the mortar has not yet been cleaned by the boy

Seeing the sentence in chunks often makes long Latin sentences much easier to read.

Because in Latin, indirect statement usually does not use a separate word like English that.

English says:

• The teacher says that the bowls were washed

Latin instead says:

• The teacher says the bowls to have been washed

That sounds unnatural in English, but it is the normal Latin pattern:

• accusative + infinitive

So the idea of English that is built into the construction itself.

In this sentence, it most naturally goes with scutellas ... lotas esse.

So the sense is:

• the bowls were washed after dinner

not necessarily:

• the teacher speaks after dinner

Word order in Latin is flexible, but readers usually connect a time phrase like post cenam with the nearby action unless something strongly suggests otherwise.

The main verb is narrat = she reports/is reporting, which is present.

The infinitives lotas esse and purgatum esse are perfect passive infinitives, so they show action completed before the time of narrat.

So the time relationship is:

• the teacher reports now
• the washing/cleaning is viewed as already completed before that reporting

With nondum, the second part is slightly nuanced: the teacher reports that the cleaning has not yet been completed.

Yes. Depending on context, narrat can be translated as:

• tells
• says
• reports
• relates
• narrates

In a sentence like this, reports or says often sounds most natural, because it introduces information in an indirect statement. The exact English choice depends on context, but the Latin grammar stays the same.