Matertera dicit fabas cum porro meliores esse quam lenticulas sine sale.

Because Latin uses an accusative-and-infinitive construction after verbs like dicit (says).

So instead of saying:

• Matertera dicit fabas... meliores esse...

Latin does not use a separate word for that plus a finite verb, the way English often does:

• Aunt says that beans are better...

Instead, Latin puts the subject of the reported statement into the accusative and the verb into the infinitive:

• fabas ... esse = that beans are
• lenticulas = the thing they are being compared to

So:

• fabae sunt = the beans are but
• dicit fabas esse = she says that the beans are

Esse is the infinitive of sum, meaning to be.

In English, we say:

• She says that beans are better...

In Latin, after dicit, the verb of the reported statement usually becomes an infinitive:

• dicit ... esse = says ... to be / says that ... are

So meliores esse means to be better.

Without esse, the sentence would be incomplete.

It actually is the correct accusative form here.

Melior, melius means better. Its feminine accusative plural form is meliores.

That happens to look the same as the nominative plural, which can be confusing.

Since fabas is:

• feminine
• plural
• accusative

the adjective agreeing with it must also be:

• feminine
• plural
• accusative

So:

• fabas meliores esse = that the beans are better

Here cum is a preposition, not a conjunction.

It means with, and it takes the ablative:

• cum porro = with leek

Yes, cum can also mean when, but only when it introduces a clause, such as:

• cum venit = when he comes

In this sentence, cum porro is clearly a prepositional phrase, so it means with leek.

Because cum takes the ablative case.

The noun is porrum (or sometimes porrus in some contexts), and here the form porro is ablative singular:

• cum porro = with leek

This is very common in Latin:

• cum amico = with a friend
• cum aqua = with water
• cum porro = with leek

Because sine means without, and it also takes the ablative.

So:

• sal = salt
• sale = with/without salt depending on the preposition

Here:

• sine sale = without salt

Compare:

• cum sale = with salt
• sine sale = without salt

Because lenticulas is being compared directly with fabas, which is the accusative subject of the infinitive construction.

In effect, Latin is saying:

• she says [beans] to be better than [lentils]

Since fabas is accusative in the indirect statement, the noun compared with it is naturally also in the accusative here:

• fabas ... quam lenticulas

So the comparison stays neatly inside the same construction.

The comparison is between:

• fabas cum porro = beans with leek and
• lenticulas sine sale = lentils without salt

The adjective meliores agrees with fabas, so grammatically the beans are the main thing being called better. But the added phrases cum porro and sine sale show the conditions of the comparison.

So the sense is:

• beans with leek are better than lentils without salt

not:

• the leek is better and not:
• the salt is better

Because Latin often does not use a separate word corresponding to English that after verbs of saying, thinking, knowing, hearing, and so on.

English:

• She says that beans are better.

Latin:

• Dicit fabas meliores esse.

The accusative + infinitive construction does the job that English that-clause does.

So the idea of that is present in the grammar, even though no separate word appears.

Matertera specifically means a mother’s sister, so a maternal aunt.

Latin can be more precise than English here:

• matertera = mother’s sister
• amita = father’s sister

English usually just says aunt, unless the distinction matters.

Latin word order is more flexible than English word order because the grammatical endings carry a lot of the meaning.

This sentence is arranged quite naturally:

• Matertera dicit = the main statement first: Aunt says
• fabas cum porro = the thing being talked about
• meliores esse = the key judgment: to be better
• quam lenticulas sine sale = the comparison

A Latin speaker could rearrange some of these words without destroying the meaning, though the emphasis might change.

For example, the sentence could still be understood if the comparison came earlier, because the case endings show how the words relate.

Potentially, yes, depending on context.

Melior basically means better, but English may choose a more natural word depending on what is being discussed:

• better tasting
• preferable
• nicer
• superior

Still, the plain grammatical meaning is simply better. Any more specific nuance would come from context, not from the form itself.

The direct version would be:

• Fabae cum porro meliores sunt quam lenticulae sine sale.

That means:

• Beans with leek are better than lentils without salt.

Notice the changes:

Indirect statement:

• fabas ... meliores esse ... lenticulas
• accusative + infinitive

Direct statement:

• fabae ... meliores sunt ... lenticulae
• nominative + finite verb

That contrast is a very useful way to understand the grammar.

Grammatically, fabas is definitely plural accusative: beans.

However, like English beans, it could refer either to individual beans or to beans as a food item in general.

So in practice it might mean:

• actual beans
• a serving of beans
• beans as a dish

Latin often leaves that kind of practical detail to context.