Pater epistulae nomine suo subscribit et consilium magistrae probat.

Because pater is in the nominative singular, which is the normal case for the subject.

The verbs subscribit and probat are both third-person singular present, so they match a singular subject: pater.

So:

• pater = the father
• subscribit = he signs
• probat = he approves

Latin often puts the subject only once, even when it goes with two verbs.

Because subscribere commonly takes the dative, not a direct object in the accusative.

So Latin says:

• epistulae subscribere = to sign a letter / to subscribe to a letter

Even though English says sign a letter, Latin uses a different construction.

So here epistulae is dative singular, not accusative.

Subscribit is the present tense of subscribere.

Its basic literal idea is to write underneath, and in this context it means to sign or to sign at the end of.

So it does not just mean write in general. It specifically suggests adding a signature or name below the text.

Nomine is ablative singular of nomen.

The phrase nomine suo is an idiomatic way to say something like:

• in his own name
• under his own name
• with his own name

The ablative is often used for means, manner, or accompanying circumstances, and this phrase tells us how the father signs.

Because suus, sua, suum is the reflexive possessive adjective. It refers back to the subject of the clause.

Here the subject is pater, so:

• nomine suo = with his own name

If Latin used eius, it would usually mean his in the sense of someone else's, not the subject's own.

So suo is exactly what we expect here.

It agrees grammatically with nomine, not with pater.

Agreement in Latin means matching gender, number, and case with the noun it modifies:

• nomine = ablative singular neuter
• suo = ablative singular neuter

But in meaning, suo refers back to pater, the subject.

So:

• grammatical agreement: with nomine
• logical reference: back to pater

Here magistrae is best understood as genitive singular:

• consilium magistrae = the teacher's plan/advice

That is a very common Latin pattern: a noun followed by a genitive showing possession or association.

In isolation, magistrae could also be dative singular, but in this sentence the genitive makes the best sense.

Because probat already has its direct object: consilium.

So the structure is:

• consilium = what he approves
• magistrae = whose plan/advice it is

If magistrae were dative, we would expect it to mean something like for the teacher or to the teacher, but that does not fit naturally with probat here.

So consilium magistrae is most naturally the teacher's advice/plan.

Consilium can have a wider range of meanings than one single English word. Depending on context, it can mean:

• plan
• advice
• decision
• counsel

So if your translation gives plan or advice, either can be reasonable depending on the context of the passage.

This is common in Latin: one word often covers a broader semantic range than its nearest English equivalent.

Because Latin has no articles.

So a noun like pater can mean:

• the father
• a father

Likewise:

• epistulae = to the letter or to a letter
• magistrae = of the teacher or of a teacher

Context tells you which English article to use in translation.

Latin word order is much more flexible than English word order because the endings show how the words function.

In this sentence:

• pater is clearly the subject because it is nominative
• epistulae is dative
• consilium is accusative
• magistrae is genitive

So Latin does not need a fixed English-style order to make the meaning clear.

The sentence places the verbs subscribit and probat late in the clause, which is very common in Latin.

Yes.

Latin often gives the subject once and then uses it with multiple coordinated verbs:

• Pater ... subscribit
• et ... probat

So the father both:

• signs the letter
• approves the teacher's plan/advice

There is no need to repeat pater before the second verb.

It goes with subscribit.

It tells you how the father signs:

• subscribit nomine suo = he signs with his own name

It does not describe the letter itself. So nomine suo belongs with the action of signing, not with epistulae.