Sponsa cum consobrina diu loquitur, antequam ad vestibulum exeat.

Because cum can be either:

• a preposition meaning with, or
• a conjunction meaning when/since/although

Here it is followed by consobrina, a noun, so it is clearly the preposition cum = with.

So:

• cum consobrina = with her cousin

If it meant when, you would expect cum to introduce a whole clause, not just a noun.

Cum as a preposition takes the ablative case, so consobrina is ablative singular.

Its basic dictionary form is consobrina, but first-declension nouns have:

• nominative singular: consobrina
• ablative singular: consobrina

So the form happens to look the same in nominative and ablative, but its role here is ablative because of cum.

Consobrina means female cousin.

Latin often distinguishes masculine and feminine forms more explicitly than English:

• consobrinus = male cousin
• consobrina = female cousin

So cum consobrina specifically means with her female cousin.

Because loquitur comes from loquor, which is a deponent verb.

A deponent verb:

• has passive-looking forms
• but an active meaning

So:

• loquitur looks like he/she is spoken
• but actually means he/she speaks or he/she talks

This is very common in Latin, and loquor is one of the most important deponent verbs to learn.

Loquitur is:

• present tense
• third person singular
• indicative mood

So it means:

• she speaks
• she is speaking
• she talks

The subject is sponsa, so loquitur means the bride talks/is talking.

Because sponsa is in the nominative singular, which is the normal case for the subject of a sentence.

So:

• sponsa = the bride as subject
• loquitur = talks
• together: the bride talks

Latin often places the subject first, but it does not have to. The form of the noun, not just the word order, tells you its role.

Diu is an adverb meaning for a long time or a long time.

It modifies loquitur, telling you how long the action lasts:

• diu loquitur = she talks for a long time

It does not change form, because adverbs do not decline like nouns and adjectives.

Exeat is present subjunctive, and that is very common after antequam.

Latin often uses:

• antequam
  • subjunctive

when the action in the before-clause is viewed as anticipated, not yet realized, or simply as part of the sentence’s perspective rather than as a plain reported fact.

So:

• antequam ad vestibulum exeat = before she goes out to the vestibule

The subjunctive here does not necessarily make the meaning dramatic in English; it is just normal Latin usage.

Exeat is:

• present tense
• third person singular
• subjunctive mood
• from exeo, exire = go out, exit

So it means she may go out / she go out / she goes out, depending on context. In this sentence, natural English is simply:

• before she goes out

Because it is third person singular, its understood subject is most naturally sponsa.

The preposition ad takes the accusative case and usually means to or toward.

So:

• ad vestibulum = to the vestibule/entrance hall

Vestibulum is neuter, and here it is in the accusative singular, which for many second-declension neuter nouns looks the same as the nominative singular.

No. Antequam can take either the indicative or the subjunctive.

Very broadly:

• indicative: the action is presented more straightforwardly as an actual fact
• subjunctive: the action is viewed as anticipated, intended, or not yet realized from the standpoint of the main clause

In practice, Latin often uses the subjunctive after antequam, so exeat is not surprising at all.

In this sentence, the most natural understanding is yes.

Latin often leaves the subject unspoken when it is easy to infer from context. Since exeat is third person singular and sponsa is the main subject, the reader normally understands:

• before the bride goes out to the vestibule

Could Latin specify another subject? Yes, but then it would usually make that clearer.

Latin word order is much freer than English word order because Latin uses case endings and verb endings to show grammatical relationships.

English relies heavily on position:

• The bride talks with her cousin

Latin can move parts around more flexibly:

• Sponsa cum consobrina diu loquitur
• Diu sponsa cum consobrina loquitur
• Cum consobrina sponsa diu loquitur

These can all mean basically the same thing, though different orders may slightly change emphasis.

In your sentence, the order is quite natural:

• subject first: sponsa
• accompanying phrase: cum consobrina
• adverb: diu
• verb: loquitur
• then the before-clause

It breaks down like this:

• Sponsa = subject
• cum consobrina = prepositional phrase, with her cousin
• diu = adverb, for a long time
• loquitur = main verb, talks
• antequam ad vestibulum exeat = subordinate clause, before she goes out to the vestibule

So the sentence has:

• a main clause: Sponsa cum consobrina diu loquitur
• a subordinate clause introduced by antequam: antequam ad vestibulum exeat

That is a very common and useful Latin sentence pattern.