Το πάνω συρτάρι είναι άδειο, αλλά το κάτω είναι γεμάτο.

Greek normally uses the definite article much more often than English.

Here, το πάνω συρτάρι means the upper/top drawer.
The article το is needed because we are talking about a specific drawer.

A bare form like πάνω συρτάρι would usually not sound natural in this sentence.

Here they mean:

• πάνω = upper / top
• κάτω = lower / bottom

So:

• το πάνω συρτάρι = the top drawer
• το κάτω = the bottom one

These words can also function as adverbs in other contexts, where they mean up / upstairs / above and down / downstairs / below.
In this sentence, though, they are being used to describe which drawer is meant.

Because Greek, like English, can leave out a noun when it is already understood.

So:

• το κάτω είναι γεμάτο

really means:

• το κάτω συρτάρι είναι γεμάτο

This is exactly like English the bottom one is full, where one stands in for drawer. Greek often just uses the article + adjective/adverb-like word and leaves the noun understood.

They agree with συρτάρι, which is a neuter singular noun.

• συρτάρι = a drawer, neuter singular
• άδειο = empty, neuter singular
• γεμάτο = full, neuter singular

Their basic dictionary forms are usually:

• άδειος = empty
• γεμάτος = full

But because συρτάρι is neuter, the adjective changes to:

• άδειο
• γεμάτο

Yes, το συρτάρι is a neuter noun.

That is why the article is το, and why the adjectives are in neuter singular:

• το πάνω συρτάρι
• το κάτω
• άδειο
• γεμάτο

Greek normally repeats the verb here:

• Το πάνω συρτάρι είναι άδειο, αλλά το κάτω είναι γεμάτο.

This is the most natural full version.

You may sometimes hear ellipsis in informal speech, but for learners it is best to keep the verb in both parts when making a contrast like this.

αλλά means but.

It is the normal conjunction for a direct contrast:

• Το πάνω συρτάρι είναι άδειο, αλλά το κάτω είναι γεμάτο.

Another contrast word you may meet is όμως, which often means however or though, but αλλά is the straightforward choice here.

Because κάτω here is one of those words that does not change form, while the article shows the gender, number, and case.

So you get:

• το κάτω συρτάρι = the lower drawer
• ο πάνω όροφος = the upper floor
• η κάτω πόρτα = the lower door

Notice that πάνω and κάτω stay the same, but the article changes:

• ο
• η
• το

Yes, absolutely.

That is the full, explicit version:

• Το πάνω συρτάρι είναι άδειο, αλλά το κάτω συρτάρι είναι γεμάτο.

Greek often omits the repeated noun because it is obvious from context. Both versions are correct; the shorter one is simply more natural in this situation.

The stress is:

• Το ΠΑ-νω συρ-ΤΑ-ρι εί-ΝΑΙ Α-δει-ο, αλ-ΛΑ το ΚΑ-τω εί-ΝΑΙ γε-ΜΑ-το.

More simply:

• πάνω → stress on the first syllable
• συρτάρι → stress on τά
• είναι → stress on εί
• άδειο → stress on ά
• αλλά → stress on the second syllable
• κάτω → stress on the first syllable
• γεμάτο → stress on μά

Because άδειο and γεμάτο are not directly modifying the noun inside the noun phrase here. They are part of the predicate after είναι.

So the structure is:

• Το πάνω συρτάρι = the subject
• είναι άδειο = is empty

and

• το κάτω = the subject
• είναι γεμάτο = is full

This is the same basic pattern as English The drawer is empty.

In other contexts, yes. These words are very common and can have several related meanings.

For example:

• πάνω στο τραπέζι = on the table
• κάτω από το τραπέζι = under the table

But in το πάνω συρτάρι and το κάτω συρτάρι, they clearly mean upper/top and lower/bottom because they are identifying one drawer in relation to another.

You can add a phrase after γεμάτο.

For example:

• Το κάτω είναι γεμάτο ρούχα. = The bottom one is full of clothes.
• Το κάτω είναι γεμάτο με χαρτιά. = The bottom one is full of papers.

So γεμάτο can stand alone, as in your sentence, or be followed by what the object is full of.

Yes, the main noun phrases here are nominative because they are the subjects of είναι.

• Το πάνω συρτάρι = nominative subject
• το κάτω = nominative subject, with συρτάρι understood

The predicate adjectives άδειο and γεμάτο also match the subject in gender and number, so they appear in the neuter singular form.