En la terminal, miramos la pantalla hasta que aparece la puerta de embarque de nuestro vuelo.

Because mirar means to look at or to watch, while ver means to see.

Here the idea is that we are actively looking at the screen, so miramos la pantalla is the natural choice.

• mirar la pantalla = to look at the screen
• ver la pantalla = to see the screen

So miramos focuses on the action of watching the information board.

Because hasta on its own is usually followed by a noun or time expression, but when it introduces a whole clause with a conjugated verb, Spanish normally uses hasta que.

Compare:

• hasta las cinco = until five
• hasta mañana = until tomorrow
• hasta que aparece la puerta = until the gate appears

So the que is required here because aparece la puerta de embarque... is a full clause.

In this sentence, aparece is used because the sentence describes something as a real, normal event: we watch the screen until the gate appears.

With hasta que, Spanish often uses:

• indicative when the action is seen as factual, habitual, or already viewed as part of a real sequence
• subjunctive when the action is still in the future from the speaker’s point of view

So:

• Miramos la pantalla hasta que aparece... = We watch the screen until it appears.
  This sounds like a routine or general description.
• Miraremos la pantalla hasta que aparezca... = We will watch the screen until it appears.
  Here the appearance is still future, so the subjunctive is natural.

Because the subject is singular: la puerta de embarque de nuestro vuelo.

The main noun is puerta, which is singular, so the verb must also be singular:

• la puerta ... aparece
• not la puerta ... aparecen

Even though the phrase is long, the real subject is still just one gate.

Yes. In airport Spanish, puerta de embarque is the standard expression for boarding gate or simply gate.

Literally:

• puerta = door/gate
• embarque = boarding

So la puerta de embarque is the place where passengers board the plane.

In English we just say gate, but Spanish often uses the fuller expression.

De nuestro vuelo means of our flight or for our flight in the sense of the gate associated with our flight.

This is very natural in Spanish. It identifies which boarding gate we mean:

• la puerta de embarque de nuestro vuelo = the boarding gate of our flight / our flight’s gate

You may also hear para nuestro vuelo in some contexts, but de nuestro vuelo is very idiomatic here because it links the gate directly to the flight.

Because en expresses location: in the terminal or at the terminal.

• en la terminal = in/at the terminal
• a la terminal would suggest movement toward the terminal

So if you are already there and describing what happens there, en is the correct preposition.

Yes, here terminal is feminine, so Spanish uses la terminal.

In the context of airports, terminal is commonly feminine:

• la terminal del aeropuerto

That is the standard form you should learn for this meaning.

Spanish often uses the present tense to describe:

• habitual actions
• routines
• general situations
• vivid narration

So miramos and aparece make the sentence sound like a typical sequence of events:

• We are in the terminal.
• We watch the screen.
• The gate appears.

It is not necessarily happening right this second; it can also mean this is what we do.

Here la pantalla refers to the airport information screen or departures board.

Spanish often uses pantalla for display screens in general. In an airport context, it naturally means the screen where flight information appears.

So miramos la pantalla means we look at the departures/flight information screen.

The comma separates the opening location phrase from the main clause.

• En la terminal, miramos la pantalla...

This is similar to English when we begin with a setting or time phrase:

• At the terminal, we watch the screen...

The comma is not absolutely the most important part of the sentence, but it helps mark En la terminal as background information before the main action.