Antequam currus moveatur, auriga equam et mulum iungit.

Because auriga is one of those Latin nouns that is first declension in form but masculine in gender.

So:

• auriga = nominative singular
• it is the subject of iungit
• its -a ending does not make it feminine

Latin has several masculine first-declension nouns, especially for jobs or social roles, such as poeta, agricola, and nauta.

Here currus is nominative singular, because it is the subject of moveatur.

That may feel strange to an English speaker, because the cart is receiving the action. But that is exactly how the passive voice works:

• active: someone moves the cart
• passive: the cart is moved

In Latin, the receiver of the action becomes the grammatical subject in a passive clause, so it goes into the nominative.

Also, currus is a fourth-declension noun. Without macrons, currus can look ambiguous, but the verb moveatur is singular, so here currus must be singular too. If it were plural, you would expect moveantur.

Because Latin often uses the subjunctive after antequam when the action is viewed as anticipated, pending, or not yet realized at the time of the main action.

So the sense is not just a flat statement of fact, but something like:

• before the cart is moved
• before the cart can be set in motion

If Latin wanted to present the action more simply as a straightforward fact, movetur could appear in other contexts. But here moveatur gives the clause a more prospective feeling.

Moveatur is:

• present
• subjunctive
• passive
• third person singular

from moveo, movere = move

So literally it means something like:

• may be moved
• is to be moved
• in smoother English here, is moved or moves, depending on how the sentence is being translated

The important point is that the Latin form itself is passive.

Because they are the direct objects of iungit.

• equa becomes equam in the accusative singular
• mulus becomes mulum in the accusative singular

So the driver is yoking:

• the mare
• and the mule

Those are the things directly affected by iungit.

Iungit comes from iungo, which basically means join, yoke, or harness.

In this sentence, it most naturally means that the driver yokes or harnesses the mare and the mule as a team.

Latin often leaves some details understood from context. So even if the sentence does not explicitly say to the cart, the idea can still be:

• the driver yokes the mare and mule together
• or yokes them for the cart

The cases and verb forms tell you.

Clause 1:

• Antequam currus moveatur
• currus is nominative, so it is the subject of moveatur

Clause 2:

• auriga equam et mulum iungit
• auriga is nominative, so it is the subject of iungit
• equam and mulum are accusative, so they are the objects

So there are two different subjects:

• currus in the subordinate clause
• auriga in the main clause

That is very normal in Latin.

Yes. Latin word order is much freer than English word order because the endings already show the grammatical roles.

This sentence begins with the antequam clause because it sets the time frame first:

• Before the cart is moved...

Then the main clause follows:

• the driver yokes the mare and the mule

Also, putting the verb iungit at the end is very common in Latin.

Latin could rearrange the words for emphasis without changing the basic meaning, as long as the forms stay clear.

Because equa means mare, a female horse.

By contrast:

• equus = horse, often specifically a male horse
• equa = mare

So equam is simply the accusative singular of equa.

This is not a special construction; it is just the vocabulary choice in the sentence.

Because Latin usually does not need subject pronouns unless they are being emphasized.

The verb endings already tell you enough:

• iungit = he/she/it yokes
• moveatur = it may be moved / is moved

So Latin can leave the pronouns unstated:

• auriga already tells you who performs iungit
• currus already tells you what is the subject of moveatur

That is much more normal in Latin than it is in English.