Είναι αδύνατο να προλάβω το τρένο σήμερα.

Είναι αδύνατο is an impersonal expression meaning it is impossible.

Greek often uses the neuter singular adjective in this kind of impersonal statement:

• Είναι δύσκολο = It is difficult
• Είναι εύκολο = It is easy
• Είναι αδύνατο = It is impossible

So αδύνατο is neuter because it is not describing a specific masculine or feminine noun. It works like English it is impossible, where it is just a dummy subject.

να introduces a clause with a verb and is one of the most important words in Modern Greek.

In this sentence:

• να προλάβω = to catch / for me to catch / that I catch

It does not work exactly like the English infinitive to, because Modern Greek usually does not use an infinitive the way English does. Instead, Greek uses να + a finite verb form.

So:

• Είναι αδύνατο να προλάβω...
  literally works more like
• It is impossible that I catch...
  but in natural English we say
• It is impossible for me to catch...

This is about aspect.

• προλάβω is the perfective form after να
• προλαβαίνω is the imperfective form

Here, catching the train is seen as a single complete event: either you make it or you do not. That is why Greek uses να προλάβω.

So:

• να προλάβω το τρένο = to manage to catch the train / to make the train

If you used να προλαβαίνω, it would sound wrong in this context, because you are not talking about an ongoing or repeated action.

Many learners first meet this as the aorist subjunctive form.

Here προλάβω means something like:

• catch
• make
• manage to get in time for

So προλάβω το τρένο does not mean physically grab the train. It means arrive in time before it leaves.

The verb προλαβαίνω often has the idea of being in time, managing before it is too late, or getting something done in time.

The I is built into the verb form προλάβω.

Greek verbs usually show the subject clearly through their endings, so the subject pronoun is often omitted.

• προλάβω = I catch / I manage to catch in this kind of clause

You could say να προλάβω εγώ or να προλάβω το τρένο εγώ, but that would add emphasis, something like:

• for me to catch the train
• I’m the one who can’t catch the train

In normal speech, Greek usually leaves εγώ out.

Το τρένο is the direct object of προλάβω.

• το = the
• τρένο = train

The noun τρένο is neuter, and in this case the nominative and accusative forms are the same:

• το τρένο = the train

So even though it is the object, it looks the same as it would as a subject.

Yes, σήμερα can move.

The sentence as given:

• Είναι αδύνατο να προλάβω το τρένο σήμερα.

usually means:

• It’s impossible for me to catch the train today.

But Greek word order is flexible, and moving σήμερα can change emphasis:

• Σήμερα είναι αδύνατο να προλάβω το τρένο.
  = Today, it’s impossible for me to catch the train.

• Είναι αδύνατο σήμερα να προλάβω το τρένο.
  = similar meaning, with more focus on today

The original version is very natural.

Yes, usually it is.

• Δεν μπορώ να προλάβω το τρένο σήμερα.
  = I can’t catch the train today.

• Είναι αδύνατο να προλάβω το τρένο σήμερα.
  = It’s impossible for me to catch the train today.

The second one sounds stronger and more absolute. It suggests there is really no chance.

So if you want to sound more emphatic, είναι αδύνατο is a good choice.

You could as a grammar aid, but it is not the most natural English translation.

A more natural English version is:

• It is impossible for me to catch the train today. or
• There’s no way I can catch the train today.

Literal translations can help you understand the Greek structure, but natural translations are better for real usage.

Yes, very often. It is a common pattern.

For example:

• Είναι αδύνατο να έρθω. = It’s impossible for me to come.
• Είναι αδύνατο να το κάνουμε σήμερα. = It’s impossible for us to do it today.
• Είναι αδύνατο να ξέρει. = It’s impossible that he knows / He can’t possibly know.

So the pattern is:

• Είναι αδύνατο + να + verb

It is a very useful structure to learn.

Yes. Αδύνατον also exists and means the same thing, but αδύνατο is the more everyday Modern Greek form.

So:

• Είναι αδύνατο να προλάβω το τρένο σήμερα.
  is the most natural everyday version.

You may still see or hear αδύνατον, especially in more formal, literary, or fixed expressions.