Uxor promittit se cras ad mercatum venturam esse.

Because se is the reflexive pronoun. It refers back to the subject of the main verb, which is uxor.

So in this sentence:

• uxor promittit = the wife promises
• se ... venturam esse = that she will come

Since the she inside the reported statement is the same person as uxor, Latin uses se.

If it meant The wife promises that another woman will come, Latin would use something like eam instead.

This is the future infinitive, and Latin uses it in indirect statement to show an action that is future relative to the main verb.

After verbs like promittit (promises), Latin often does not use that + finite verb the way English does. Instead, it uses:

• an accusative subject +
• an infinitive

Here that gives:

• se = the subject of the indirect statement
• venturam esse = to be about to come / will come

So se venturam esse means that she will come.

Venturam is the future active participle of venire (to come).

Its basic forms are:

• venturus masculine
• ventura feminine
• venturum neuter

Here it appears as venturam because it agrees with se, which refers to uxor, a feminine singular noun. In indirect statement, the subject is in the accusative, so the feminine singular accusative form is venturam.

So:

• se = herself, accusative
• venturam = about to come, feminine singular accusative
• esse = to be

Together: se venturam esse = that she will come

Because it must agree with the implied subject se, which refers to uxor.

Agreement here is in:

• gender: feminine
• number: singular
• case: accusative

So the participle must be feminine singular accusative, which is venturam.

If the subject were masculine, you would get venturum esse.
If it were plural feminine, you would get venturas esse, and so on.

Because the normal future infinitive in Latin is formed with:

• the future participle
• plus esse

So:

• venturam esse = to be going to come / will come

Without esse, the expression would be incomplete in standard prose.

Think of venturam esse as one unit: the infinitive form needed after promittit in indirect statement.

They belong to two different grammatical layers of the sentence.

The main clause is:

• uxor promittit = the wife promises

Here uxor is the subject of the main verb, so it is nominative.

Inside the indirect statement, Latin uses the accusative-and-infinitive construction:

• se cras ad mercatum venturam esse

In that construction, the subject of the infinitive is put in the accusative, so we get se, not a nominative form.

Mercatum is accusative singular.

It is accusative because it follows the preposition ad, which takes the accusative when it means to, toward.

So:

• ad mercatum = to the market

This phrase shows motion toward a place.

Because ad commonly expresses movement toward a place.

So:

• ad = to, toward
• mercatum = market

Together: ad mercatum = to the market

English learners sometimes expect a bare dative or something similar, but with ordinary destination phrases like this, ad + accusative is very common.

Cras is an adverb meaning tomorrow.

It does not change form, and it does not agree with anything. It simply tells you when the coming will happen.

So:

• se cras ad mercatum venturam esse = that she will come to the market tomorrow

Yes. Latin word order is much more flexible than English word order.

This sentence could be rearranged in several ways without changing the basic meaning, for example:

• Uxor se cras ad mercatum venturam esse promittit
• Cras uxor se ad mercatum venturam esse promittit
• Uxor promittit cras se ad mercatum venturam esse

The usual differences are mostly about emphasis or style, not core meaning.

That said, the given order is perfectly natural.

Because Latin normally does not use that in this kind of construction.

In English we say:

• The wife promises that she will come

But Latin often prefers indirect statement, which uses:

• accusative subject
  • infinitive

So instead of a conjunction meaning that, Latin says:

• se ... venturam esse

This is one of the most important sentence patterns in Latin.

Promittit is present tense, so it most directly means she promises or she is promising.

Depending on context, the English translation could be:

• The wife promises that she will come to the market tomorrow
• The wife is promising that she will come to the market tomorrow

Latin present tense can cover both a simple present and a progressive present, depending on context.

Because Latin has no articles.

There is no direct equivalent of English the or a/an. Whether a noun is understood as definite or indefinite depends on context.

So:

• uxor can mean wife or the wife
• mercatus/mercatum can mean market or the market

In this sentence, English naturally uses the wife and the market, but Latin does not need separate words for that.