Μετά από αϋπνία δύο νυχτών, το πρωινό ξύπνημα είναι πολύ δύσκολο.

Μετά από means after.

In Modern Greek, από normally takes the accusative. So the noun after it is in the accusative case.

Here that noun is αϋπνία. Its nominative and accusative singular forms are the same, so you do not see a visible change:

• nominative: η αϋπνία
• accusative: την αϋπνία

So in this sentence, μετά από αϋπνία = after insomnia / after sleeplessness.

The two dots over υ are called a diaeresis. They show that α and υ are pronounced separately, not as the usual letter combination αυ.

So:

• αυ is normally pronounced as one unit
• αϋ tells you: pronounce them separately

That is why αϋπνία is not read like a normal αυ- word.

A rough pronunciation is:

• αϋπνία ≈ a-ip-NEE-a

The stress falls on -νί-.

Because νυχτών is in the genitive plural.

The phrase αϋπνία δύο νυχτών literally means something like:

• insomnia of two nights
• sleeplessness lasting two nights

So δύο νυχτών depends on αϋπνία and specifies its extent/duration.

A few useful points:

• δύο does not change form for gender or case
• νυχτών is the genitive plural of νύχτα

So:

• nominative plural: δύο νύχτες
• genitive plural: δύο νυχτών

A little, yes.

The noun is η νύχτα (night), but in some forms the stem changes to νυχτ-.

For example:

• nominative singular: η νύχτα
• accusative singular: τη νύχτα
• nominative plural: οι νύχτες
• genitive plural: των νυχτών

So νυχτών may look surprising at first, but it is the normal genitive plural form.

Ξύπνημα is a noun meaning:

• waking
• waking up
• the act of getting awake

It comes from the verb:

• ξυπνάω / ξυπνώ = to wake up

So:

• ξυπνάω το πρωί = I wake up in the morning
• το πρωινό ξύπνημα = the morning waking / waking up in the morning

In this sentence, it refers to the experience or act of waking up in the morning.

Because Greek uses the definite article much more often than English.

In English, you might say:

• Waking up in the morning is very difficult

But Greek often prefers:

• Το πρωινό ξύπνημα είναι πολύ δύσκολο

So the article το does not necessarily mean a specific one-time waking. It can also be used for a general idea or activity.

Because πρωινό is an adjective agreeing with ξύπνημα.

• ξύπνημα is neuter singular
• so the adjective must also be neuter singular

That gives:

• masculine: πρωινός
• feminine: πρωινή
• neuter: πρωινό

So:

• το πρωινό ξύπνημα = the morning waking

For the same reason: it agrees with the subject, which is το πρωινό ξύπνημα.

Since ξύπνημα is neuter singular, the predicate adjective must also be neuter singular:

• δύσκολος = masculine
• δύσκολη = feminine
• δύσκολο = neuter

So:

• Το ξύπνημα είναι δύσκολο.
• Η μέρα είναι δύσκολη.
• Ο δρόμος είναι δύσκολος.

Here πολύ means very, so it is functioning as an adverb and modifies δύσκολο.

• πολύ δύσκολο = very difficult

That is different from πολύς / πολλή / πολύ, which can also be an adjective meaning much / many / a lot of.

Compare:

• πολύ δύσκολο = very difficult
• πολλή δουλειά = a lot of work

So in this sentence, πολύ is the fixed adverb form.

Yes. Greek word order is fairly flexible.

The given sentence begins with:

• Μετά από αϋπνία δύο νυχτών, ...

This puts the condition/background first: after two nights of insomnia, then the main statement follows.

You could also say:

• Το πρωινό ξύπνημα είναι πολύ δύσκολο μετά από αϋπνία δύο νυχτών.

That keeps the same basic meaning, but the original version sounds a bit more natural if you want to emphasize the cause first.

The sentence is correct and natural, but it sounds a bit written or formal because of αϋπνία δύο νυχτών.

In everyday speech, many speakers might say something more direct, such as:

• Μετά από δύο νύχτες χωρίς ύπνο, το πρωινό ξύπνημα είναι πολύ δύσκολο.
• Μετά από δύο νύχτες χωρίς ύπνο, είναι πολύ δύσκολο να ξυπνήσεις το πρωί.

So the original sentence is good Greek, but slightly more polished or literary than casual conversation.