Ayer me pasé media hora esperando a que la pantalla dejara de parpadear.

Because pasarse + amount of time + gerund is a very common way to say to spend time doing something.

So:

• Pasé media hora = I spent half an hour / half an hour passed
• Me pasé media hora esperando = I spent half an hour waiting

That little me is part of the idiomatic expression pasarse here. In this sentence, me pasé media hora is the natural way to say that the speaker spent that amount of time on the activity.

It means I spent half an hour.

The structure is:

pasarse + time expression + gerund

Examples:

• Me pasé dos horas estudiando = I spent two hours studying
• Nos pasamos toda la tarde hablando = We spent the whole afternoon talking

In your sentence:

• me pasé = I spent
• media hora = half an hour
• esperando... = waiting...

So the whole chunk means I spent half an hour waiting...

Because hora is feminine, and here medio/media means half and agrees with the noun.

So:

• media hora = half an hour
• medio día = half a day / noon
• media manzana = half an apple

This is different from medio used as an adverb, which does not change:

• medio cansado
• medio dormida

But with nouns, when it means half, it agrees:

• media hora
• medio litro

Because the sentence uses the pattern pasarse + time + gerund, which focuses on how the time was spent.

So:

• me pasé media hora esperando = I spent half an hour waiting

The gerund esperando works like waiting in English after spent:

• I spent half an hour waiting

You could say other things, but they would sound different:

• Esperé media hora = I waited half an hour
• Me pasé media hora esperando = I spent half an hour waiting

Both are correct, but the second one emphasizes the experience of time passing while doing the action.

Yes, absolutely.

That would mean essentially the same thing:

• Ayer esperé media hora... = Yesterday I waited half an hour...
• Ayer me pasé media hora esperando... = Yesterday I spent half an hour waiting...

The difference is mainly one of perspective:

• esperé media hora focuses more directly on the action of waiting
• me pasé media hora esperando highlights the amount of time that got used up in that activity

The version with me pasé can feel a bit more expressive, as if the speaker is stressing how long it felt.

Because when esperar is followed by a new clause with a different subject, Spanish normally uses esperar a que + subjunctive.

Here the subject of esperando is I, but the subject of dejara is la pantalla. Since the subject changes, Spanish uses:

esperar a que + verb

So:

• Esperé a que llegara = I waited for him/her to arrive
• Estoy esperando a que me llamen = I’m waiting for them to call me

In your sentence:

• esperando a que la pantalla dejara de parpadear

If the subject stays the same, Spanish often uses an infinitive instead:

• Estoy esperando para salir = I’m waiting to leave

Because it comes after esperar a que, which normally requires the subjunctive when you are talking about something awaited, not yet achieved at that point.

The speaker was waiting for the screen to stop flickering. That stopping was something hoped for or awaited, so Spanish uses the subjunctive:

• esperar a que + subjunctive

Examples:

• Espero a que venga = I’m waiting for him/her to come
• Esperaba a que terminara = I was waiting for it to finish

In your sentence:

• esperando a que la pantalla dejara de parpadear

The stopping of the flickering was still pending during the waiting.

Because of sequence of tenses.

The main action is in the past:

• Ayer me pasé... = Yesterday I spent...

After a past-tense verb like that, Spanish normally uses the imperfect subjunctive in this kind of subordinate clause:

• present / future main verb -> often present subjunctive
• past main verb -> often imperfect subjunctive

Compare:

• Espero a que la pantalla deje de parpadear = I’m waiting for the screen to stop flickering
• Esperaba / me pasé... esperando a que la pantalla dejara de parpadear = I was waiting / I spent... waiting for the screen to stop flickering

So dejara is the expected tense here.

Yes. Dejara and dejase are both forms of the imperfect subjunctive.

So both are correct:

• a que la pantalla dejara de parpadear
• a que la pantalla dejase de parpadear

In modern usage, -ra forms such as dejara are generally more common, but -se forms are also perfectly valid and are used in Spain as well.

There is no important meaning difference here.

Dejar de + infinitive means to stop doing something.

So:

• dejar de fumar = to stop smoking
• dejar de hablar = to stop talking
• dejar de parpadear = to stop blinking/flickering

In this sentence, la pantalla dejara de parpadear means that the screen would stop flickering.

This is a very common structure in Spanish.

Yes, literally parpadear means to blink, especially with eyes. But it is also commonly used for lights, screens, cursors, etc., to mean to blink, flash, or flicker.

So for a screen:

• la pantalla parpadea = the screen is blinking/flickering

Depending on context, English might translate it as:

• blink
• flash
• flicker

Here, flicker is often the most natural translation.

Spanish usually uses the definite article more often than English.

So where English might say:

• waiting for the screen to stop flickering

Spanish naturally says:

• esperando a que la pantalla dejara de parpadear

The article la is normal here because the speaker has a specific screen in mind.

Dropping the article would generally sound unnatural in this sentence.

Yes, it can go elsewhere. Spanish word order is flexible.

These are all possible:

• Ayer me pasé media hora esperando...
• Me pasé media hora ayer esperando...
• Me pasé ayer media hora esperando...

Putting Ayer first is very natural because it sets the time frame immediately: Yesterday...

That is probably the most neutral and common order here.

Both are natural, and both are common in Spain.

They are very close, but there is a slight nuance:

• Me pasé media hora esperando = I spent half an hour waiting
• Estuve media hora esperando = I was waiting for half an hour

Me pasé emphasizes that the time got used up in that activity. Estuve describes the duration of the state or action.

In everyday speech, either one could work well in this context.