Mater fenestram aperit, sed pulvis de pariete in mensam cadit.

Because fenestram is the direct object of aperit. It is the thing being opened, so Latin puts it in the accusative case.

• fenestra = window, in the nominative
• fenestram = window, in the accusative

So Mater fenestram aperit means Mother opens the window, where mother is the subject and window is the object.

Mater is nominative singular, the subject of aperit. It means mother.

It may look unusual if you are expecting first- or second-declension endings, but mater is a third-declension noun. Its dictionary form is already mater, and that is also its nominative singular form. So the sentence does not need to change it.

Both are third person singular present active indicative verbs.

• aperit = she opens or he opens
• cadit = it falls, he falls, or she falls

In this sentence:

• mater ... aperit = mother opens
• pulvis ... cadit = dust falls

Latin usually does not need a separate word for she, he, or it, because the verb ending already tells you the person and number.

Because pulvis is in the nominative singular, and it is the thing doing the action of cadit.

So in sed pulvis de pariete in mensam cadit:

• pulvis = the dust
• cadit = falls

That makes pulvis the subject: the dust falls.

Because the preposition de takes the ablative case. So pariete is ablative singular.

• paries = wall
• pariete = from the wall / off the wall, after de

This is a very common thing to learn in Latin: many prepositions require a particular case, and de is one that takes the ablative.

Because in can take two different cases, depending on the meaning:

• in + accusative = motion into or onto
• in + ablative = location in or on

Here the dust is moving and falls onto the table, so Latin uses in mensam.

Compare:

• in mensam cadit = it falls onto the table
• in mensa est = it is on the table

It means the dust falls from the wall onto the table.

The phrase has two parts:

• de pariete = from/off the wall
• in mensam = onto the table

So Latin is showing both the starting point and the destination of the movement.

Latin word order is more flexible than English word order because Latin uses case endings to show how words function in the sentence.

English depends heavily on position:

• Mother opens the window is different from The window opens the mother

Latin does not depend on word order in the same way, because mater is nominative and fenestram is accusative. So even if the order changed, the endings would still tell you who is doing the action and what is being acted on.

Still, the given order is perfectly natural and clear.

Not usually. Classical Latin has no definite article and no indefinite article like English the and a/an.

So:

• mater can mean mother or the mother
• fenestram can mean a window or the window
• pulvis can mean dust or the dust

The exact English wording depends on the context and on what sounds natural in translation.

Sed means but. It joins the two clauses and shows a contrast:

• Mater fenestram aperit = Mother opens the window
• sed = but
• pulvis de pariete in mensam cadit = dust falls from the wall onto the table

So the second clause is presented as something that happens in contrast or as a consequence in the scene.

Here pulvis is singular. That is why the verb is also singular: cadit.

So the phrase means dust falls or the dust falls, not dusts fall. In English, dust is usually treated as an uncountable noun, and Latin often uses the singular here in a similar way.

Yes, to a large extent. Because Latin uses case endings, several different word orders could still mean essentially the same thing.

For example, these would still be understandable:

• Fenestram mater aperit
• Pulvis in mensam de pariete cadit

The endings still show the grammar:

• mater = subject
• fenestram = object
• pariete = ablative after de
• mensam = accusative after in

However, word order can still affect emphasis and style, even when the basic meaning stays the same.