Η αποσκευή μου είναι ήδη στο αεροπλάνο, αλλά εγώ είμαι ακόμα στην πύλη.

Greek nouns have gender and their articles change according to gender, number, and case.

In this sentence:

• η αποσκευή = feminine singular, nominative
• το αεροπλάνο = neuter singular
• την πύλη = feminine singular, accusative

Why?

• Η αποσκευή μου is the subject of the first clause, so it is in the nominative.
• After σε (in / at / on), Greek normally uses the accusative, so:
  • σε το αεροπλάνο → στο αεροπλάνο
  • σε την πύλη → στην πύλη

So the article changes because the grammar around the noun changes.

In Greek, the unstressed possessive forms such as μου, σου, του, της usually come after the noun.

So:

• η αποσκευή μου = my bag / my luggage
• η πτήση μου = my flight
• το διαβατήριό μου = my passport

This is the normal pattern in Greek.

If you want extra emphasis, you can use δικός:

• η δική μου αποσκευή

That sounds more like my own bag or my bag specifically.

Yes. They are both forms of είμαι (to be), but they match different subjects.

• Η αποσκευή μου είναι...
  The subject is η αποσκευή (my luggage/bag), which is third person singular, so Greek uses είναι.

• εγώ είμαι...
  The subject is I, which is first person singular, so Greek uses είμαι.

So:

• είμαι = I am
• είναι = he/she/it is

Yes, Greek often drops subject pronouns because the verb ending already shows the person.

So είμαι ακόμα στην πύλη already means I am still at the gate.

But here εγώ is included for contrast:

• Η αποσκευή μου είναι ήδη στο αεροπλάνο, αλλά εγώ είμαι ακόμα στην πύλη.

This gives the sense of:

• My luggage is already on the plane, but I am still at the gate.

So εγώ is there not because it is required, but because it adds emphasis and contrast.

They express two different time ideas:

• ήδη = already
• ακόμα = still (in this sentence)

So:

• Η αποσκευή μου είναι ήδη στο αεροπλάνο = my luggage is already on the plane
• εγώ είμαι ακόμα στην πύλη = I am still at the gate

This creates a contrast:

• the luggage has already moved ahead
• the speaker is still behind

Important note: ακόμα can also mean even in other contexts, but here it clearly means still.

Greek uses σε very broadly. It can cover meanings that English divides into in, on, and at.

So σε + article can mean:

• in
• on
• at

depending on the context.

Examples:

• στο αεροπλάνο = on the plane
• στο λεωφορείο = on the bus
• στο σπίτι = at home / in the house
• στην τράπεζα = at the bank

So Greek does not always match English prepositions one-for-one.

They are contracted forms of σε + article.

• σε + το → στο
• σε + την → στη(ν) / στην
• σε + τον → στον

So in your sentence:

• στο αεροπλάνο = σε το αεροπλάνο
• στην πύλη = σε την πύλη

These contractions are completely normal and are what you usually say in everyday Greek.

The final -ν in την / στην is often kept before:

• vowels
• κ, π, τ
• μπ, ντ, γκ
• ξ, ψ

Since πύλη starts with π, the natural form is:

• στην πύλη

You may also see στη in some contexts before other sounds, but here στην is the standard form.

In Modern Greek, σε normally takes the accusative, even when it expresses location.

So both of these are accusative phrases:

• στο αεροπλάνο
• στην πύλη

This is different from some older stages of Greek and from languages that use a separate locative idea more visibly. In Modern Greek, σε + accusative covers most meanings like to, in, at, on.

Greek word order is fairly flexible, but the version you have is very natural and neutral.

The sentence:

• Η αποσκευή μου είναι ήδη στο αεροπλάνο, αλλά εγώ είμαι ακόμα στην πύλη.

sounds like a standard, clear way to say it.

You can move some elements for emphasis, for example:

• Ήδη η αποσκευή μου είναι στο αεροπλάνο...
• ...αλλά ακόμα είμαι στην πύλη.
• ...αλλά στην πύλη είμαι ακόμα εγώ.

But these shifts change the focus or emphasis. For a learner, the original order is the safest and most natural one to copy.

Not exactly.

• αποσκευή means luggage / baggage / a piece of luggage
• βαλίτσα means suitcase

So αποσκευή is a bit more general and is especially natural in travel or airport contexts.

At an airport, you often hear things related to:

• χειραποσκευή = carry-on baggage
• αποσκευή = luggage / checked baggage

If the speaker specifically meant a suitcase, they could say βαλίτσα, but αποσκευή fits the airport setting very well.