Πήγα να χάσω το τρένο, αλλά τελικά είχε καθυστέρηση.

In this sentence, πήγα να + verb is an idiomatic way to say I almost..., I was on the verge of..., or I nearly...

So:

• Πήγα να χάσω το τρένο = I almost missed the train

It does not literally mean I went to miss the train.

This pattern is very common in Greek:

• Πήγα να πέσω. = I almost fell.
• Πήγα να τρελαθώ. = I nearly went crazy.

So it often expresses something that was very close to happening, but did not happen in the end.

Because πηγαίνω / πάω can sometimes lose its literal meaning of go and become part of an expression.

Here, πήγα να... does not describe physical movement. It functions more like:

• I almost...
• I was about to...

This is one of those cases where Greek uses a verb in a way English does not.

So although πήγα is the past form of πάω, in this expression you should learn it as a chunk:

• πήγα να + verb = I almost / I was close to...

Because after να, Greek normally uses the subjunctive form, not the ordinary past tense.

So:

• να χάσω = subjunctive form
• έχασα = simple past, I missed

In other words:

• Πήγα να χάσω το τρένο = I almost missed the train
• Έχασα το τρένο = I missed the train

A useful thing to notice is that after να, Greek often uses a form that looks like the aorist stem:

• να δω
• να φύγω
• να χάσω

So χάσω here does not by itself mean future. It is simply the correct form after να.

Να is a very common particle in Greek. It often introduces:

• the subjunctive
• a desired action
• a possible action
• an intended action

In this sentence, να introduces the action that almost happened:

• πήγα να χάσω = I almost came to miss

You do not usually translate να word-for-word. Its role is grammatical rather than lexical.

English often uses different structures where Greek uses να:

• Θέλω να φύγω. = I want to leave.
• Μπορώ να έρθω; = Can I come?
• Πήγα να χάσω το τρένο. = I almost missed the train.

Το τρένο is in the accusative case because it is the direct object of χάνω (to miss / to lose).

The basic pattern is:

• χάνω κάτι = I miss / lose something

So:

• χάνω το τρένο = I miss the train

Since τρένο is a neuter noun, the nominative and accusative singular look the same:

• nominative: το τρένο
• accusative: το τρένο

That is why the form does not change here.

Τελικά means something like:

• in the end
• after all
• eventually
• as it turned out

In this sentence, it marks the final outcome:

• I almost missed the train, but in the end it was delayed.

It is a very useful adverb in everyday Greek.

Examples:

• Τελικά δεν ήρθε. = In the end, he/she didn’t come.
• Τελικά όλα πήγαν καλά. = In the end, everything went well.

Because Greek often uses the expression:

• έχει καθυστέρηση = it has a delay / it is delayed

So:

• Το τρένο έχει καθυστέρηση. = The train is delayed.
• Το τρένο είχε καθυστέρηση. = The train was delayed / had a delay.

This is very natural Greek, especially in everyday speech and announcements.

You could also hear:

• Το τρένο καθυστέρησε. = The train was late / got delayed
• Το τρένο ήταν καθυστερημένο. = The train was delayed

But είχε καθυστέρηση is extremely common and idiomatic.

Because the Greek expression here is based on have:

• έχει καθυστέρηση = has a delay

So in the past it becomes:

• είχε καθυστέρηση

If you said ήταν, you would need a different structure, for example:

• Ήταν καθυστερημένο. = It was delayed.

So both ideas are possible in Greek, but they use different grammar:

• είχε καθυστέρηση = it had a delay
• ήταν καθυστερημένο = it was delayed

Because Greek often omits subject pronouns and even repeated nouns when the subject is clear from context.

In the sentence:

• Πήγα να χάσω το τρένο, αλλά τελικά είχε καθυστέρηση.

the subject of είχε is understood to be το τρένο.

Greek does this all the time. English usually repeats the subject:

• ...but in the end it was delayed.

Greek can simply leave it implied:

• ...αλλά τελικά είχε καθυστέρηση.

You could say:

• ...αλλά τελικά το τρένο είχε καθυστέρηση.

But that sounds more explicit and slightly less natural unless you want emphasis.

Είχε is the imperfect of έχω. Here it describes a situation or state in the past:

• the train was in a state of delay
• the train had a delay

The imperfect is natural because the delay is being presented as a background situation that explains why the speaker did not miss the train.

Compare:

• είχε καθυστέρηση = it was delayed / it had a delay
• καθυστέρησε = it got delayed / it was delayed as a completed event

So είχε καθυστέρηση focuses more on the condition, not on the event of becoming delayed.

Yes. That is another very common way to say I almost missed the train.

Compare:

• Πήγα να χάσω το τρένο
• Παραλίγο να χάσω το τρένο

Both are natural.
A rough difference is:

• παραλίγο να is a very direct, standard way to say almost
• πήγα να can feel a little more vivid or conversational, as if the event was very close to happening

In many contexts, they are interchangeable.

Usually not in normal context. Native speakers recognize πήγα να + verb as a fixed expression very easily.

If you wanted a truly literal meaning involving movement and purpose, Greek would normally say something else more clearly, such as:

• πήγα για να...
• πήγα να το προλάβω depending on context

So in your sentence, a Greek speaker will understand πήγα να χάσω idiomatically, not literally.

It breaks down like this:

• Πήγα να χάσω το τρένο

  • πήγα να χάσω = I almost missed
  • το τρένο = the train

• αλλά

  • but

• τελικά είχε καθυστέρηση

  • τελικά = in the end / as it turned out
  • είχε καθυστέρηση = it was delayed / it had a delay

So the structure is:

• I almost missed the train, but as it turned out, it was delayed.

You would say:

• Έχασα το τρένο. = I missed the train.

That is different from:

• Πήγα να χάσω το τρένο. = I almost missed the train.

So the contrast is important:

• έχασα = it actually happened
• πήγα να χάσω = it almost happened, but did not

That is one of the key things this sentence teaches.