Fama de nova magistra in foro est.

Because fama is the subject of the sentence.

• fama = nominative singular
• It is the thing that est says exists or is located somewhere

So in this sentence, fama is the main noun the sentence is about.

Because they are not the subject. They are part of the prepositional phrase de nova magistra.

The preposition de takes the ablative case, so both words after it must be ablative:

• magistra = ablative singular
• nova = ablative singular feminine, agreeing with magistra

So the phrase means about the new teacher, and the case is determined by de, not by the role of subject.

Here de means about or concerning.

So:

• de magistra = about the teacher
• de nova magistra = about the new teacher

This is a very common use of de in Latin.

Because in can take two different cases depending on the meaning:

• in + ablative = in / on a place, with no motion
• in + accusative = into / onto a place, with motion toward it

Here the idea is location, not movement:

• in foro = in the forum

If someone were moving into the forum, Latin would use the accusative instead.

foro is the ablative singular of forum.

• dictionary form: forum
• ablative singular: foro

Since it follows in in the sense of location, it must be ablative.

Latin often uses simple is where English prefers there is.

So Fama ... est can be understood naturally as:

• Rumor is ...
• or, in better English, There is a rumor ...

Latin does not need a separate word for there in this kind of sentence.

Because Classical Latin does not have articles like English does.

So fama could mean:

• a rumor
• the rumor
• sometimes just rumor in a more general sense

Likewise in foro can mean in the forum or in a forum, depending on context. The surrounding context tells you which is most natural.

Because adjectives in Latin agree with the nouns they describe in:

• gender
• number
• case

Here:

• magistra is feminine, singular, ablative
• nova is also feminine, singular, ablative

That matching tells you nova describes magistra.

Yes. magistra is the feminine form.

• magister = male teacher / master
• magistra = female teacher / mistress / female instructor, depending on context

So this sentence is specifically about a woman.

Latin word order is more flexible than English word order because the endings show grammatical roles.

So Fama de nova magistra in foro est could be rearranged in other ways without changing the basic meaning very much, for example:

• In foro fama de nova magistra est
• De nova magistra fama in foro est

The original order is perfectly normal, but Latin often moves words around for emphasis, style, or rhythm.

fama can have several related meanings, such as:

• rumor
• report
• news
• reputation
• fame

In this sentence, because of the structure fama de ..., the most natural sense is something like rumor or report about someone.

So the context determines which English word is best.

Yes:

• fama — nominative singular feminine, subject, from fama
• de — preposition taking the ablative, meaning about
• nova — ablative singular feminine adjective, modifying magistra
• magistra — ablative singular feminine noun, object of de
• in — preposition taking the ablative here, meaning in
• foro — ablative singular of forum
• est — third person singular present of esse, meaning is

That structure is what gives the sentence its meaning.