Έχοντας στρώσει το κρεβάτι, τίναξα το πάπλωμα και άνοιξα λίγο το παράθυρο να μπει αέρας.

It is a non-finite introductory clause meaning something like having made the bed.

• έχοντας = having
• στρώσει = the participle form used here after έχοντας
• το κρεβάτι = the bed

So the structure έχοντας + participle often corresponds to English having done... or sometimes simply after doing....

In this sentence, it sets up an action that happened before the main actions:

• Having made the bed, I shook the duvet and opened the window a little...

This structure is quite common in written Greek and in more careful speech.

Because these two forms express different ideas.

1. έχοντας στρώσει

This means having made the bed / after making the bed.
It suggests the action was completed first.

2. στρώνοντας

This means making the bed / while making the bed.
It usually suggests an action in progress or something happening at the same time.

So:

• Έχοντας στρώσει το κρεβάτι, ... = After I had made the bed, ...
• Στρώνοντας το κρεβάτι, ... = While I was making the bed, ...

In your sentence, the speaker first finished making the bed, and then did the next actions, so έχοντας στρώσει fits better.

Yes, normally it does.

In Greek, when you use έχοντας + participle, the understood subject is usually the same as the subject of the main verb.

So here:

• Έχοντας στρώσει το κρεβάτι, τίναξα...
• The person who made the bed is also the person who shook the duvet and opened the window.

That is the natural reading.

English has a similar issue:

• Having made the bed, I opened the window = fine
• Having made the bed, the window was opened = awkward, because it sounds like the window made the bed

So Greek learners should watch for that same-subject relationship.

They are in the aorist past because the sentence describes completed actions.

• τίναξα = I shook
• άνοιξα = I opened

The aorist in Greek is very often used for single, complete events in the past.

That fits this sentence well:

1. I made the bed.
2. I shook the duvet.
3. I opened the window a little.

These are presented as a sequence of finished actions.

If the imperfect were used instead, it would suggest ongoing, repeated, or background actions, which would sound different.

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

For example:

• τίναξα already means I shook
• άνοιξα already means I opened

So εγώ is unnecessary unless you want emphasis or contrast.

Compare:

• Τίναξα το πάπλωμα. = I shook the duvet.
• Εγώ τίναξα το πάπλωμα. = I was the one who shook the duvet / I shook the duvet (not someone else).

Omitting the pronoun is the normal Greek pattern.

It means to make the bed.

Literally, στρώνω has a broader meaning like spread, lay out, or arrange, but with το κρεβάτι it specifically means make the bed.

So:

• στρώνω το κρεβάτι = I make the bed
• έστρωσα το κρεβάτι = I made the bed
• έχοντας στρώσει το κρεβάτι = having made the bed

This is a standard everyday expression.

It means I shook the duvet/quilt.

The verb τινάζω means shake, shake out, or sometimes dust off, depending on context.

Here, τίναξα το πάπλωμα suggests the speaker gave the duvet a shake, probably to fluff it up or straighten it on the bed.

Vocabulary:

• πάπλωμα = duvet, quilt, sometimes comforter depending on the variety of English

So this is a very natural household action:

• make the bed
• shake the duvet
• open the window a little

Because λίγο here modifies the verb phrase and means a little / slightly.

So:

• άνοιξα λίγο το παράθυρο = I opened the window a little

This word order is very natural in Greek.

You may also hear:

• άνοιξα το παράθυρο λίγο

but άνοιξα λίγο το παράθυρο is smoother and more common in this kind of sentence.

Notice that λίγο does not mean for a little while here. It means the window was opened slightly, not briefly.

It expresses purpose: so that some air could come in / to let air in.

So:

• άνοιξα λίγο το παράθυρο να μπει αέρας
• literally: I opened the window a little so that air might enter

In natural English, we might say:

• I opened the window a little to let some air in

In Greek, να + verb is very common after another verb when expressing purpose, intention, or desired result.

Because να μπει uses the perfective subjunctive, which is the normal choice here for a single, complete event: air entering.

Breakdown:

• μπει = subjunctive form of μπαίνω (enter/go in)
• να μπει αέρας = for air to come in

Why not the others?

να μπει

Used for a single intended event:

• open the window so that air can come in

να μπαίνει

This would suggest a more ongoing or repeated sense:

• so that air keeps coming in It is possible in some contexts, but it sounds different.

να μπήκε

This is not right here. After να, Greek uses subjunctive forms, not a past form like that.

So να μπει αέρας is exactly what you would expect after άνοιξα το παράθυρο in this context.

Because Greek often leaves out the article with a noun when it is meant in a general or indefinite sense.

Here, αέρας means air in general, not the air as a specific identified thing.

So:

• να μπει αέρας = to let some air in

This is very natural Greek.

If you said να μπει ο αέρας, it would sound more specific, as if referring to the air/wind in a more definite way, and in this sentence that is less natural.

The comma separates the introductory participial phrase from the main clause.

So:

• Έχοντας στρώσει το κρεβάτι, = introductory background action
• τίναξα το πάπλωμα και άνοιξα... = main actions

This is similar to English punctuation in:

• Having made the bed, I shook the duvet...

The comma helps the reader see the sentence structure clearly.

Yes, Greek word order is fairly flexible, though some versions sound more natural than others.

The original sentence is very natural:

• Έχοντας στρώσει το κρεβάτι, τίναξα το πάπλωμα και άνοιξα λίγο το παράθυρο να μπει αέρας.

Possible variations include:

• Τίναξα το πάπλωμα και άνοιξα λίγο το παράθυρο να μπει αέρας, έχοντας στρώσει το κρεβάτι.

• grammatical, but less natural in everyday flow

• Άνοιξα λίγο το παράθυρο να μπει αέρας και τίναξα το πάπλωμα.
• also grammatical, but now the order of actions is presented differently

Greek allows movement for emphasis, rhythm, and style, but the original ordering is the clearest if you want to show a neat sequence of actions.

It is correct and natural, but it can sound a bit more written or narrative than the most casual everyday speech.

A very common everyday alternative would be:

• Αφού έστρωσα το κρεβάτι, τίναξα το πάπλωμα και άνοιξα λίγο το παράθυρο να μπει αέρας.

That means:

• After I made the bed, I shook the duvet and opened the window a little to let some air in.

So:

More written / compact

• Έχοντας στρώσει το κρεβάτι...

More everyday / straightforward

• Αφού έστρωσα το κρεβάτι...

Both are good Greek; the difference is mainly one of style.