Κάνω ώρα να κοιμηθώ όταν έχει θόρυβο στη γειτονιά.

It is an idiomatic expression meaning I take a while or it takes me some time.

So:

• Κάνω ώρα να κοιμηθώ = I take a while to fall asleep

Literally, κάνω means I do / I make, and ώρα means time / hour, but together here they do not mean I make time. It is a fixed everyday expression.

You can also hear:

• Κάνω πολλή ώρα να κοιμηθώ = I take a long time to fall asleep
• Έκανα ώρα να κοιμηθώ = It took me a while to fall asleep

In Modern Greek, verbs often connect to another verb with να instead of using an infinitive like English does.

So where English says:

• to fall asleep

Greek says:

• να κοιμηθώ

After expressions like κάνω ώρα, θέλω, μπορώ, πρέπει, Greek normally uses να + verb.

Because κοιμηθώ refers to falling asleep / getting to sleep, while κοιμάμαι refers more to being asleep / sleeping.

Here the idea is:

• It takes me a while to fall asleep

not:

• It takes me a while to be sleeping

So να κοιμηθώ is the right choice.

A useful contrast:

• κοιμάμαι = I sleep / I am sleeping
• να κοιμηθώ = to fall asleep / to get to sleep

It is the 1st person singular aorist subjunctive form of κοιμάμαι.

That sounds technical, but the important point is this:

• aorist aspect here gives the idea of a single completed event: fall asleep
• subjunctive is used because it comes after να

So να κοιμηθώ means something like:

• for me to fall asleep
• more naturally in English: to fall asleep

Because Greek usually does not need subject pronouns when the verb ending already shows the subject.

Here:

• κάνω = I do / I take
• κοιμηθώ = I fall asleep

So the I is already built into the verb forms.

You could say Εγώ κάνω ώρα να κοιμηθώ..., but that would usually add emphasis, like:

• As for me, I take a while to fall asleep...

Όταν means when.

In this sentence it has a general / habitual meaning:

• when there is noise in the neighborhood
• in other words, whenever there is noise in the neighborhood

So the sentence describes something that usually happens, not just one specific occasion.

Both are possible, but έχει θόρυβο is very natural in everyday Greek.

Here έχει is being used in an impersonal way to mean:

• there is noise

So:

• όταν έχει θόρυβο = when there is noise

You could also say:

• όταν υπάρχει θόρυβος

That is also correct, but έχει θόρυβο sounds very common and conversational.

Because έχει takes a direct object, so the noun goes in the accusative case.

• ο θόρυβος = nominative
• τον θόρυβο / θόρυβο = accusative

So:

• έχει θόρυβο = literally it has noise, meaning there is noise

If you used υπάρχει, then you would normally use the nominative:

• υπάρχει θόρυβος

Στη γειτονιά means in the neighborhood.

It is made from:

• σε = in / at / to
• τη = the (feminine accusative article)

These combine into:

• στη

And:

• γειτονιά = neighborhood

So:

• στη γειτονιά = in the neighborhood

Because after σε, Greek uses the accusative.

The dictionary form is:

• η γειτονιά = the neighborhood

After σε:

• σε τη γειτονιά → στη γειτονιά

This is completely normal Greek grammar.

Yes. Greek word order is more flexible than English word order.

This sentence could also be:

• Όταν έχει θόρυβο στη γειτονιά, κάνω ώρα να κοιμηθώ.

That means the same thing. The difference is mostly one of emphasis or style.

The original sentence starts with the main idea:

• I take a while to fall asleep

and then adds the situation:

• when there is noise in the neighborhood

It means some time / a while. It does not always have to mean a very long time, though in practice it often suggests that something is not quick.

If you want to make the idea stronger, you can say:

• Κάνω πολλή ώρα να κοιμηθώ = I take a long time to fall asleep
• Κάνω αρκετή ώρα να κοιμηθώ = I take quite a while to fall asleep

So the sentence without πολλή is natural, but a little less emphatic.

It most naturally describes a usual / repeated situation.

Because of όταν plus the general context, it means something like:

• Whenever there is noise in the neighborhood, it takes me a while to fall asleep.

If you wanted to talk about one specific night, Greek would often use other time markers, for example:

• Σήμερα κάνω ώρα να κοιμηθώ, γιατί έχει θόρυβο στη γειτονιά.
• Tonight it’s taking me a while to fall asleep because there is noise in the neighborhood.

Yes. A few alternatives are:

• Αργώ να κοιμηθώ όταν έχει θόρυβο στη γειτονιά.
  = I’m slow to fall asleep / It takes me a long time to fall asleep...

• Δυσκολεύομαι να κοιμηθώ όταν έχει θόρυβο στη γειτονιά.
  = I have trouble falling asleep when there is noise...

• Δεν μπορώ να κοιμηθώ εύκολα όταν έχει θόρυβο στη γειτονιά.
  = I can’t fall asleep easily when there is noise...

Your original sentence is perfectly natural; these just give slightly different shades of meaning.