Dux femina milites monet ne sine ordine procedant.

Because femina is in apposition to dux.

• dux = leader
• femina = woman

Both are nominative singular and refer to the same person. Latin often uses a second noun to clarify or add information about the first noun. So dux femina means something like the leader, a woman or more naturally the woman leader / the female leader.

No. dux is a noun that can refer to either a male or a female leader. Its grammatical form does not change here just because the person is female.

Latin often uses the same noun for both sexes, and if the writer wants to make the sex explicit, they can add a word like femina.

So:

• dux = leader
• dux femina = a leader who is a woman

No. femina is a noun, not an adjective.

An adjective meaning female would be something like feminea in some contexts, but here Latin uses the noun femina in apposition to dux.

So this is not leader female with an adjective; it is more like leader, woman.

Because milites is the direct object of monet.

• monet = warns / advises
• the person being warned is put in the accusative

So:

• dux femina = the subject
• milites = the soldiers, the people she warns

That is why it is milites rather than nominative militēs—though in spelling they look the same. What tells you its function is the sentence structure and the verb.

Because the subject is singular: dux femina refers to one person.

Even though there are two nominative words, they describe the same person, not two separate people. So the verb stays singular:

• dux femina ... monet = the female leader warns

If there were two separate subjects, the verb would be plural.

Because after monet Latin uses a subjunctive clause here for what is being urged or warned.

The structure is:

• monet ne + subjunctive

This means warns/advises ... not to ...

So:

• procedant is present subjunctive, 3rd person plural
• it matches the understood subject milites

This is a very common Latin construction for a negative command reported indirectly.

Because ne is the normal word for negative purpose or negative command-like clauses with the subjunctive.

Here the idea is not simple factual negation (they do not proceed), but rather:

• she warns them not to proceed

That kind of clause uses ne, not non.

So:

• non procedunt = they do not proceed
• ne procedant = that they should not proceed / not to proceed

Because its understood subject is milites.

Even though milites appears in the main clause as the object of monet, it is also the logical subject of the subordinate clause:

• The female leader warns the soldiers
• that they should not advance

So procedant is 3rd person plural: they should advance / in this sentence, that they should not advance.

Ordine is ablative singular because it follows the preposition sine.

The preposition sine always takes the ablative and means without.

So:

• sine ordine = without order

Depending on context, this can mean without orderliness, without formation, or out of formation.

Literally, it means without order.

In a military sentence like this, it often has a more specific sense such as:

• without formation
• without discipline
• out of ranks
• in a disorderly way

So it is not just abstract order in a broad sense; it can suggest marching or advancing properly in formation.

It comes from procedo, procedere, processi, processum, meaning go forward, advance, or proceed.

In this sentence, the military context makes advance a very natural translation.

So ne sine ordine procedant means something like:

• not to advance without formation
• not to move forward in disorder

Because Latin often expresses this idea with ne + subjunctive instead of an infinitive.

English prefers:

• warns the soldiers not to advance

Latin here prefers:

• warns the soldiers that they should not advance

That is why the clause has a finite subjunctive verb (procedant) rather than an infinitive.

The basic relationships are shown mostly by case endings and verb forms, so Latin word order is more flexible than English word order.

Here the sentence is arranged quite naturally:

• Dux femina — subject first
• milites — object next
• monet — main verb
• ne sine ordine procedant — subordinate clause at the end

This order is clear and fairly straightforward, but Latin could rearrange parts of it for emphasis.

Dux is a third-declension noun.

Its principal forms are:

• nominative singular: dux
• genitive singular: ducis

Many third-declension nouns have nominative singular forms that are less predictable than first- and second-declension nouns. So dux is just the normal nominative singular form, even though it may look unusual at first.

Yes. That is a very good literal explanation of the grammar.

A more natural English translation might be:

• The female leader warns the soldiers not to advance without formation
• The woman leader warns the soldiers not to proceed in disorder

But your very literal version captures the structure of the Latin well.