Discipula amicae suae in via occurrit et epistulam ostendit.

Because the verb occurrere takes the person encountered in the dative in Latin.

So:

• discipula = the schoolgirl, student
• amicae suae = to her friend

Even though English says she meets her friend, Latin uses a different construction: literally something like she runs into her friend with friend in the dative.

This is one of those verb patterns that English speakers simply have to learn.

Amicae suae is dative singular feminine.

You can tell because:

• amicae can be dative singular
• suae agrees with amicae in gender, number, and case
• the verb occurrit strongly suggests a dative object

So the two words go together as one phrase: to her friend.

Latin uses suus, sua, suum when the possessor is the subject of the clause.

Here, the subject is discipula, so if the friend belongs to or is associated with the subject, Latin normally says:

• amica sua = her own friend

In this sentence, suae refers back to discipula.

By contrast, eius would usually mean his/her friend, referring to someone else, not the subject.

So:

• amicae suae = to her own friend / to her friend where her means the schoolgirl
• amicae eius = to her friend where her means some other female person

Because in with the ablative often expresses location: in/on/at a place.

So:

• in via = on the road / in the street

If in took the accusative, it would usually suggest motion into something rather than location.

Compare:

• in via = on the road
• in viam = onto the road / into the street depending on context

Here the idea is location, so the ablative is used.

Here occurrit comes from occurrere, which commonly means:

• to meet
• to run into
• to come upon

A useful thing to remember is that it is not constructed like English meet. In Latin, the person encountered is in the dative.

So discipula amicae suae occurrit means the schoolgirl meets/runs into her friend.

Epistulam is accusative singular because it is the direct object of ostendit.

The verb ostendere means to show, and the thing shown is put in the accusative.

So:

• epistula = a letter
• epistulam = the letter, as direct object

In other words, the schoolgirl shows a letter.

Yes. The subject is still discipula.

Latin often does not repeat the subject if it stays the same. So the sentence works like this:

• Discipula ... occurrit = The schoolgirl meets ...
• et epistulam ostendit = and shows a letter

The subject she is understood with the second verb.

Both occurrit and ostendit can be either present or perfect in form.

That is a very common point of confusion for learners.

For example:

• occurrit can mean she meets or she met
• ostendit can mean she shows or she showed

The same is true because some Latin verb forms look identical in the 3rd person singular present and 3rd person singular perfect.

So the correct translation depends on context. If the meaning has already been given to the learner, that context decides whether the sentence is present-time or past-time.

Because the verb ending already tells you the person and number.

Both occurrit and ostendit are 3rd person singular, so Latin does not need to add a separate pronoun unless it wants emphasis.

So instead of saying she meets with an explicit she, Latin can simply say occurrit.

This is very normal in Latin.

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

In English, word order does a lot of the work:

• The girl meets her friend

In Latin, endings tell you who is subject, object, dative, and so on, so the words can be arranged more freely.

Here:

• discipula is nominative, so it is the subject
• amicae suae is dative, so it goes with occurrit
• epistulam is accusative, so it is the object of ostendit

The order may reflect style, rhythm, or emphasis, not just basic grammar.

Yes. Et means and, and here it links two actions done by the same subject:

• she meets her friend
• and she shows a letter

So the structure is basically:

• [subject] + [first verb phrase] + et + [second verb phrase]

Grammatically, suae agrees with amicae, not with discipula.

That means it matches amicae in:

• gender: feminine
• number: singular
• case: dative

However, in meaning, suae refers back to the subject, which is discipula.

So:

• agreement: with amicae
• reference: back to discipula

That is an important distinction in Latin grammar.

Yes. Latin word order is flexible, so in via could be placed in a different position without changing the basic meaning.

For example, Latin authors might move it for emphasis or style.

The important thing is that:

• in
  • ablative = location
• via is ablative singular here

So wherever the phrase appears, it still means on the road / in the street.