Candidata prudens esse dicitur, et multi cives ei favent.

Because candidata is the subject of dicitur.

In Latin, dicitur means is said. So the sentence is structured as:

• Candidata = the candidate
• dicitur = is said
• prudens esse = to be prudent

So literally: The candidate is said to be prudent.

A very helpful comparison is:

• Active: Aliqui candidātam prudentem esse dīcunt = Some people say that the candidate is prudent
• Passive: Candidāta prudēns esse dīcitur = The candidate is said to be prudent

In the active version, candidātam is accusative.
In the passive version, that same idea becomes the subject, so it changes to nominative: candidāta.

Because prudens agrees with candidata.

It is describing the candidate, and in this passive construction the candidate is nominative, so the adjective is nominative as well:

• candidata = nominative singular
• prudens = nominative singular

In the active version, you would get:

• candidātam prudentem esse dīcunt

There, both words are accusative because they belong to the accusative-and-infinitive construction after dīcunt.

So:

• candidata prudens esse dicitur = passive
• candidātam prudentem esse dicunt = active

Esse is there because Latin is using an infinitive construction after a verb of saying.

• prudens esse = to be prudent

So candidata prudens esse dicitur means the candidate is said to be prudent.

If you remove esse, prudens dicitur can still be understandable, but it more strongly suggests something like she is called prudent or she is spoken of as prudent. With esse, the structure is clearer and more standard for is said to be...

So esse helps mark the full idea:

• dicitur + infinitive = is said to ... / is said to be ...

Dicitur is the 3rd person singular present passive indicative of dico, meaning say.

So:

• dicit = he/she says
• dicitur = he/she is said

Since the subject is candidata, it means:

• candidata dicitur = the candidate is said

The present tense here gives the sense is said or is being said.

Not all Latin adjectives have different masculine and feminine forms in the nominative singular.

Prudens is a third-declension adjective of one termination, which means the nominative singular is the same for masculine and feminine:

• masculine: prudens
• feminine: prudens
• neuter: prudens

So even though candidata is feminine, prudens does not change its nominative singular form.

This is completely normal for many third-declension adjectives.

Because faveo takes the dative, not the accusative.

In English we say favor her, using a direct object.
But in Latin, favere works more like be favorable to someone.

So:

• ei = to her / for her
• favent = they favor

Literally, multi cives ei favent is something like:

• many citizens are favorable to her

But the natural English translation is simply:

• many citizens favor her

So eam would be wrong here, because faveo does not take a direct object.

Ei is the dative singular form of the pronoun is, ea, id.

Here it means:

• to her
• or, more naturally in English, her

Since candidata is feminine singular, ei refers back to her.

A useful thing to remember is that ei can mean:

• to him
• to her
• to it

The context tells you which one is meant. Here it clearly means to her.

They are nominative plural, because they are the subject of favent.

• multi = many
• cives = citizens
• favent = favor

So multi cives are the people doing the action.

Both words agree:

• multi = nominative plural masculine
• cives = nominative plural

Together: many citizens

Civis can be masculine or feminine, depending on the person meant. It is a third-declension noun meaning citizen.

Here multi cives is masculine plural in form because it either refers to male citizens or to a mixed group, which Latin normally treats as masculine plural.

So:

• civis = citizen
• cives = citizens

This is the regular nominative plural form.

Latin word order is more flexible than English word order because the endings show what each word is doing.

So although the sentence is written:

• Candidata prudens esse dicitur, et multi cives ei favent

Latin could move parts around without changing the basic meaning, for example:

• Multi cives candidatae favent would mean something slightly different in form but same basic idea if the pronoun were replaced properly
• Ei multi cives favent
• Prudens esse candidata dicitur

The original order is natural because:

• Candidata comes first to introduce the main topic
• dicitur comes later to complete the first clause
• ei favent places the pronoun before the verb in a common Latin pattern

So word order often helps with emphasis, but the endings carry the grammar.

Yes, in an important sense.

In active Latin, verbs of saying often introduce an accusative + infinitive construction:

• Aliqui dicunt candidātam prudentem esse
• Some people say that the candidate is prudent

That is the standard indirect statement pattern.

In your sentence, that active idea has been turned into the passive:

• Candidata prudens esse dicitur

This is often called the personal passive of a verb of saying. English does the same thing:

• They say that the candidate is prudent
• The candidate is said to be prudent

So if you already know accusative-and-infinitive indirect statement, this sentence is a very useful passive version of that pattern.

The sentence does not say.

That is one reason the passive is useful here: it lets Latin express a general report without naming the speaker.

So dicitur often means something like:

• she is said
• people say
• it is said

If Latin wanted to name the speaker, it could add an agent, usually with ab + ablative in a true passive context. But very often no agent is given, because the point is simply that this is what people say.