Proscaenium ante pulpitum est.

Not necessarily. Both words are neuter singular nouns of the second declension, and in that pattern the nominative singular and accusative singular look the same.

So here:

• proscaenium = nominative singular
• pulpitum = accusative singular

This is a very common feature of neuter nouns in Latin: the nominative and accusative are always identical.

You can tell from the structure of the sentence:

• ante is a preposition
• ante takes an object, and that object is pulpitum
• that leaves proscaenium as the noun connected with est

So proscaenium is the subject, and est agrees with it in number: it is singular, so the verb is est rather than sunt.

Because ante is a preposition that takes the accusative case when it means before / in front of.

So:

• ante pulpitum = in front of the stage/platform

This is something you simply learn with the preposition: ante + accusative.

It can mean either, depending on context.

• temporal: before
• spatial: in front of

In this sentence, because it is describing where one thing is located relative to another, ante is clearly spatial: in front of.

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

So a Latin sentence like this can often be translated in more than one natural English way, depending on context:

• The proscaenium is in front of the pulpitum
• A proscaenium is in front of a pulpitum

Latin leaves that distinction unstated unless the context makes it clear.

Latin word order is much more flexible than English word order.

Placing est at the end is very normal in Latin. In fact, Latin often prefers to put the verb near the end of the sentence.

So:

• Proscaenium ante pulpitum est

is perfectly natural Latin word order.

English usually needs something more fixed, but Latin can move words around more freely because the endings show their grammatical role.

est is the third-person singular present of esse, meaning to be.

Here it links the subject to a phrase of location:

• proscaenium = subject
• ante pulpitum = where it is
• est = is

So the sentence is a simple statement of location: X is in front of Y.

Yes. It is a prepositional phrase:

• ante = preposition
• pulpitum = object of the preposition

Together they describe the location of proscaenium. So you can think of ante pulpitum as answering the question where?

Yes, very often.

For example, Latin could also say:

• Ante pulpitum proscaenium est
• Est proscaenium ante pulpitum

The basic meaning would stay the same. The differences would mostly be matters of emphasis or style, not grammar.

The original order is straightforward and natural, but it is not the only possible order.

No. It can also be an adverb.

For example:

• as a preposition: ante pulpitum = in front of the pulpitum
• as an adverb: ante = before / earlier / previously

In this sentence it is definitely a preposition, because it is followed by pulpitum.

Yes—this sentence is a good reminder of three very useful Latin points:

1. Neuter nominative and accusative are the same
2. ante takes the accusative
3. Latin often puts the verb at the end

If you notice those three things, the sentence becomes much easier to read.