Epistula subscripta in mensa posita est.

The main verb is posita est.

This is a perfect passive verb form:

• posita = placed, a perfect passive participle
• est = is

Together, they mean was placed or has been placed, depending on context.

So the core of the sentence is:

Epistula ... posita est = The letter was placed / has been placed

This is a very common Latin pattern.

In Latin, a perfect passive tense is made with:

• a perfect passive participle
• plus a form of sum (to be)

So:

• posita est literally looks like placed is
• but idiomatically it means has been placed or was placed

This is just how Latin builds the passive perfect.

A few similar examples:

• amata est = she was loved / has been loved
• scriptus est = he was written? no — better: it was written if the subject fits
• missi sunt = they were sent

Because they are doing two slightly different jobs.

• posita est forms the main verb: was placed
• subscripta modifies epistula like an adjective: the signed letter

So the sentence is essentially:

[The signed letter] was placed on the table.

However, because subscripta is also a participle, there is a sense of completed action behind it. So the phrase can also feel a bit like:

The letter, having been signed, was placed on the table.

In normal English, though, the signed letter is usually the most natural way to express it.

Because they agree with each other in gender, number, and case.

Here:

• epistula = feminine singular nominative
• subscripta = feminine singular nominative
• posita = feminine singular nominative

Latin adjectives and participles must agree with the noun they describe.

Since epistula is feminine singular nominative, the words describing it also appear in the feminine singular nominative form.

So:

• epistula subscripta = the signed letter
• epistula ... posita est = the letter ... was placed

Because it is the subject of the sentence.

The thing being talked about — the thing that was placed — is the letter.

So:

• epistula = subject = nominative

Even though the sentence is passive in English and Latin, the subject is still the thing in the nominative:

• The letter was placed...

Because in takes different cases depending on whether it shows location or motion toward something.

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

Here the idea is location:

• in mensa = on the table

If the meaning were onto the table, Latin would normally use in mensam.

So compare:

• epistula in mensa est = the letter is on the table
• epistulam in mensam posuit = he placed the letter onto the table

Yes. In Latin, in with the ablative can mean in or on, depending on context.

With a table, English usually says on the table, but Latin can still use in mensa.

So in mensa here is naturally understood as:

• on the table

Latin prepositions do not always match English prepositions one-for-one.

Because Latin has no definite or indefinite articles.

So Latin does not have separate words for:

• the
• a
• an

That means epistula could mean:

• a letter
• the letter

The context or the translation decides which is more natural in English.

It comes from subscribo, subscribere, subscripsi, subscriptus.

In this sentence, subscripta means signed.

Although the verb is historically related to writing under something, by normal usage it commonly means to sign.

So:

• epistula subscripta = the signed letter

Yes. Latin word order is much freer than English word order because the endings show the grammar.

So these could mean essentially the same thing:

• Epistula subscripta in mensa posita est
• In mensa epistula subscripta posita est
• Posita est epistula subscripta in mensa

But the word order can affect emphasis or style.

In your sentence, the order is quite natural:

• subject first: epistula
• descriptive participle: subscripta
• place phrase: in mensa
• main verb at the end: posita est

That final position for the verb is very common in Latin.

Yes, that is a possible way to bring out the participial force of subscripta.

Latin participles often sit somewhere between:

• a simple adjective
• and a more verbal idea

So epistula subscripta can be understood as:

• the signed letter or, more explicitly,
• the letter, having been signed

In most ordinary English translations, the signed letter is smoother. But grammatically, the fuller sense of a completed action is still there.

You tell from both the form and the preposition.

• mensa can be nominative singular or ablative singular
• but after in meaning location, Latin uses the ablative
• so here in mensa must be ablative

This is a very common thing in Latin: sometimes the ending alone is not enough, but the surrounding grammar makes the case clear.