Pater in tablino sedet et epistulas legit, dum filia in horto ludit.

Because pater is in the nominative case, which is the case normally used for the subject of a sentence.

In Pater in tablino sedet et epistulas legit, pater is the one doing both actions:

• sedet = sits
• legit = reads

So pater is the subject of both verbs.

Latin does not need to repeat the subject if the same person is doing both actions.

So:

• Pater in tablino sedet et epistulas legit means
• The father sits in the study and reads letters

Latin is being economical: once pater has been introduced, it can apply to both verbs.

Because epistulas is the accusative plural, used for the direct object of legit.

He is reading letters, so letters receives the action of the verb. That makes it the direct object.

• epistulae = letters as a subject
• epistulas = letters as a direct object

So:

• epistulae legunt = the letters read
• pater epistulas legit = the father reads letters

They are in the ablative case because they follow in in the sense of location.

Here:

• in tablino = in the study
• in horto = in the garden

When in means in/on and shows where something is happening, it usually takes the ablative.

Compare:

• in horto ludit = she plays in the garden
• in hortum currit = she runs into the garden

The first is location, the second would be motion toward.

Here dum means while.

It introduces a clause that describes something happening at the same time as the main action:

• Pater in tablino sedet et epistulas legit, dum filia in horto ludit.
• The father sits in the study and reads letters, while the daughter plays in the garden.

So dum links the two actions as simultaneous.

Because the sentence describes actions happening now or as a general present scene:

• sedet = is sitting / sits
• legit = is reading / reads
• ludit = is playing / plays

Latin often uses the simple present where English might use either:

• sits / is sitting
• reads / is reading
• plays / is playing

So the Latin present tense is a bit broader than the English simple present.

Because of filia, which is nominative singular and matches the verb ending.

In:

• dum filia in horto ludit

filia is the subject, and ludit is third person singular, meaning he/she/it plays.

Since filia means daughter, the natural translation is the daughter plays.

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

English depends heavily on word order:

• The father reads the letters is not the same as The letters read the father

Latin can move words around more freely because:

• pater is nominative
• epistulas is accusative

So even if the order changed, the endings would still show who is doing what.

That said, this sentence is actually fairly natural and straightforward Latin word order.

Good question. Without macrons, legit can be ambiguous in writing.

It could represent:

• legit = reads (present tense)
• lēgit = read / has read (perfect tense)

But in this sentence, the context strongly suggests the present tense:

• sedet = sits / is sitting
• legit = reads / is reading
• ludit = plays / is playing

All three actions are happening at the same time, so legit here should be understood as reads.

Because Latin has no articles.

So:

• pater can mean father, a father, or the father
• filia can mean daughter, a daughter, or the daughter

The exact English article depends on context. In this sentence, English naturally uses the:

• The father sits in the study and reads letters, while the daughter plays in the garden.

The ending -t shows third person singular: he, she, it.

So:

• sedet = he/she/it sits
• legit = he/she/it reads
• ludit = he/she/it plays

This is why Latin often does not need an expressed subject pronoun like he or she. The verb ending already gives that information.

Et simply means and. It links two actions done by the same subject:

• sedet et legit = sits and reads

It is the normal, straightforward way to join two words or clauses in Latin, just like and in English.

Yes, Latin often omits subjects when they are clear from the verb ending.

For example:

• In tablino sedet et epistulas legit
  could mean
• He/The father sits in the study and reads letters

And:

• dum in horto ludit
  could mean
• while she/the daughter plays in the garden

But in this sentence, pater and filia are included for clarity and balance.