Cum sol occiderit, convivae in atrio convenient et convivium incipient.

No. Here cum is a conjunction meaning when.

• cum
  • ablative = with
    
    • for example, cum amico = with a friend
• cum introducing a clause = when, since, or although, depending on context

In this sentence, Cum sol occiderit means When the sun has set.

So this is not a preposition; it is introducing a subordinate clause.

Occiderit is 3rd person singular future perfect active indicative from occido.

So it means:

• he/she/it will have fallen
• with sol as the subject, the sun will have set

A useful thing to know: this form can also look identical to the perfect subjunctive in some contexts. Here, however, the meaning of the sentence makes it clear that it is future perfect indicative.

Latin often uses the future perfect in a time clause when one future action will be completed before another future action happens.

That is exactly the pattern here:

• Cum sol occiderit = When the sun has set
• convivae ... convenient et ... incipient = the guests will gather and will begin...

So Latin is showing:

1. first, the sun will set
2. then, the guests will gather and begin the feast

English sometimes does something similar with when ... has set, though we often also translate more simply as when the sun sets.

Yes. Sol is nominative singular, so it is the subject of occiderit.

• sol = the sun
• occiderit = will have set

Together: the sun will have set.

It can, but only in the right context.

Occido has a range of meanings, including ideas like:

• fall down
• go down
• set (for the sun)
• in some forms and contexts, it can even be connected with kill or strike down, though that comes from a closely related verb and can be confusing for learners

Here, because the subject is sol (the sun), the meaning is clearly the sun sets/goes down.

Convivae is nominative plural.

Its job is to be the subject of both:

• convenient
• incipient

So convivae means the guests or more specifically the dinner guests / banquet guests.

Latin often uses one subject for two verbs without repeating it, just as English does:

• The guests will gather and begin the feast.

Convenient is the 3rd person plural future active indicative of convenio, convenire.

Here it means:

• they will come together
• they will gather
• they will assemble

So:

• convivae convenient = the guests will gather

It is related in origin to English convene more than to convenient, though all these words are historically connected.

This is a very common beginner trap: convenient in Latin here is a verb, not an adjective.

Because in with a fixed location takes the ablative.

Here the idea is in the atrium or in the hall/courtyard, not motion into it.

• in
  • accusative = into / onto (motion toward)
• in
  • ablative = in / on (location)

So:

• in atrium would suggest into the atrium
• in atrio means in the atrium

Since the guests are gathering in that place, the ablative is correct.

Atrio is the ablative singular of atrium, a 2nd-declension neuter noun.

Basic forms:

• nominative singular: atrium
• ablative singular: atrio

With in, it means in the atrium.

In a Roman house, the atrium is the central hall or open main area of the house.

They do look similar, but they are different words.

• convivae = guests, diners
  
  • a noun referring to people
• convivium = banquet, feast, dinner party
  
  • a noun referring to the meal/event

In this sentence:

• convivae is the subject
• convivium is the direct object

So:

• The guests will gather
• and they will begin the feast

Convivium is accusative singular.

It is accusative because it is the direct object of incipient:

• incipient = they will begin
• convivium = the feast

So the guests are doing the action of beginning, and the feast is the thing being begun.

Because convivium is a 2nd-declension neuter noun, its nominative and accusative singular are both convivium. That is normal for neuter nouns in Latin.

Inipient is the 3rd person plural future active indicative of incipio, incipere.

It means they will begin.

So:

• convivium incipient = they will begin the feast

This matches convenient, which is also future plural. The main clause is talking about what the guests will do.

Because it does not need to. Once the subject is clear, Latin often leaves it understood with the next verb.

So:

• convivae ... convenient et convivium incipient

means:

• the guests will gather and will begin the feast

English does the same thing:

• we do not normally say the guests will gather and the guests will begin the feast

The shared subject is simply understood.

Et means and, and here it joins the two future verbs:

• convenient
• incipient

So the structure is:

• The guests will gather
• and
• will begin the feast

It links two actions done by the same subject, convivae.

It is normal Latin word order, even if it does not match English exactly.

A few things to notice:

• The cum-clause comes first: Cum sol occiderit
• The main clause follows: convivae in atrio convenient et convivium incipient
• Latin often puts verbs toward the end, though this is not a fixed rule
• Latin word order is more flexible than English because the word endings show grammatical relationships

So the sentence is arranged in a very natural Latin way:

1. first the time setting: When the sun has set
2. then the main action: the guests will gather... and begin...