Hospes ad ostium appropinquat, et servus statim aperit.

Because Latin word order is flexible. Putting hospes first gives it emphasis and immediately tells you who the sentence is about.

Grammatically, hospes is the subject of appropinquat. It is in the nominative singular.

A native English speaker may expect a fixed Subject-Verb-Object order, but Latin does not depend on word order as much as English does. The endings usually tell you the grammatical role.

Yes. Hospes is one of those Latin words that can mean either guest or host, depending on context.

In this sentence, the meaning shown to the learner is presumably guest, since someone is approaching the door and the slave opens it. That makes guest the natural interpretation here.

So:

• hospes = guest here
• but in another context it could mean host

Because ad means to, toward, or up to, and it takes the accusative case.

So:

• ad = to/toward
• ostium = accusative singular of ostium, meaning door or doorway

Together, ad ostium means to the door or up to the door.

This is very common in Latin:

• ad villam = to the house / villa
• ad urbem = to the city
• ad ianuam = to the door

It is accusative because it follows the preposition ad, which regularly takes the accusative.

This is not the direct object of the sentence. It is the object of the preposition ad.

So the structure is:

• ad
  • accusative = movement toward something

That is why we get ad ostium, not ad ostio.

Appropinquat is:

• 3rd person singular
• present tense
• active voice
• from the verb appropinquare

So it means he/she/it approaches or is approaching.

The -t ending tells you it is he/she/it.

Since the subject is hospes, the verb means:

• the guest approaches

Because servus is the subject of the second verb, aperit.

The sentence has two linked clauses:

1. Hospes ad ostium appropinquat
2. et servus statim aperit

So:

• hospes is the subject of appropinquat
• servus is the subject of aperit

Both are nominative because both are subjects.

The object is not stated explicitly, but it is understood from the context: the slave is opening the door.

So aperit here effectively means:

• opens it
• that is, opens the door

Latin often leaves out words that are obvious from context. English can do this too in some situations, but Latin does it very naturally.

If the sentence wanted to say it explicitly, it might say something like:

• servus ostium statim aperit = the slave immediately opens the door

Because Classical Latin does not have articles like English the and a/an.

So:

• hospes can mean a guest or the guest
• servus can mean a slave or the slave
• ostium can mean a door or the door

You decide from the context which English article is best.

That is why one Latin sentence can be translated into English in more than one natural way.

Statim is an adverb, meaning immediately, at once, or right away.

It modifies aperit:

• servus statim aperit = the slave opens [it] immediately

Adverbs in Latin can often move around quite freely, so you might also see:

• servus aperit statim
• statim servus aperit

The meaning would stay basically the same, though the emphasis might shift slightly.

Aperit is:

• 3rd person singular
• present tense
• active voice
• from aperire = to open

So it means he/she/it opens.

Because the subject is servus, it means:

• the slave opens

The ending -it here is a present-tense ending of a verb from the 4th conjugation (aperire).

Because Latin word order is flexible. There is a tendency for verbs to come later in the clause, but this is not a strict rule.

Here we get:

• Hospes ad ostium appropinquat
• et servus statim aperit

Both are perfectly normal Latin. Latin writers choose word order for rhythm, emphasis, and style, not because they must follow a rigid English-like pattern.

A learner should focus first on:

1. identifying the case endings
2. identifying the verb endings
3. then noticing how the words are arranged

Not really. The comma is mainly a matter of punctuation in modern printed texts.

The grammar is carried by the words and their forms, not by the comma.

Et simply means and, joining the two clauses:

• the guest approaches the door
• and the slave immediately opens [it]

So the comma may help readability, but it is not essential to understanding the Latin structure.