Έχω μια απορία για αυτή τη λέξη.

Yes. Έχω means I have, and Greek very naturally uses it in expressions like:

• Έχω μια απορία. = I have a question / I’m wondering about something
• Έχω μια ερώτηση. = I have a question
• Έχω αμφιβολίες. = I have doubts

So in this sentence, Έχω is completely normal and idiomatic.

Not exactly, though it is often translated that way.

Απορία usually means something like:

• doubt
• uncertainty
• something I’m puzzled about
• a point I don’t understand

So Έχω μια απορία για αυτή τη λέξη is a bit like saying:

• I have a question about this word
• I’m unsure about this word
• There’s something I don’t understand about this word

If you wanted a more direct, neutral question, Greek often uses ερώτηση instead.

Μια is the feminine singular indefinite article here, meaning a.

So:

• μια απορία = a question / a doubt

You can sometimes omit the indefinite article in Greek, but in this sentence μια sounds natural and expected.
Έχω απορία would sound less natural in standard everyday Greek for this meaning.

Because απορία is feminine singular, the article also has to be feminine singular: μια.

Because απορία is a feminine noun.

Greek articles must agree with the noun in gender, number, and case.

Here are the singular indefinite articles:

• ένας = masculine
• μια / μία = feminine
• ένα = neuter

Since απορία is feminine, you use μια.

It is in the accusative singular because it is the direct object of Έχω.

You are literally saying:

• I have
  • a doubt/question

So μια απορία is the thing being had, which makes it the object.

For this noun, the accusative singular form is απορία.

Για usually means for, about, or regarding, depending on context.

In this sentence, it means about:

• για αυτή τη λέξη = about this word

So the structure is:

• Έχω μια απορία = I have a question/doubt
• για αυτή τη λέξη = about this word

This is a very common use of για in Greek.

Because Greek often uses a demonstrative together with the definite article.

So:

• αυτή = this
• τη = the (feminine accusative singular)
• λέξη = word

Together:

• αυτή τη λέξη = this word

This pattern is very normal in Greek:

• αυτό το βιβλίο = this book
• αυτή η πόρτα = this door
• αυτές τις μέρες = these days

English does not use both this and the together, but Greek does.

Because after για, Greek uses the accusative case, not the genitive.

So:

• η λέξη = the word, nominative
• τη λέξη = the word, accusative
• της λέξης = of the word, genitive

Since the sentence means about this word, and για takes the accusative, the correct form is:

• για αυτή τη λέξη

not

• για αυτή της λέξης

Yes. Both are possible.

You may see:

• αυτή τη λέξη
• αυτήν τη λέξη

The extra final -ν in αυτήν is often optional in modern Greek in many contexts. In everyday speech and writing, αυτή τη λέξη is very common and natural.

So for a learner, it is good to recognize both forms.

It does change by case, but in this noun the nominative and accusative singular happen to look the same.

For λέξη:

• nominative singular: η λέξη
• accusative singular: τη λέξη
• genitive singular: της λέξης

So the article changes clearly, while the noun itself stays λέξη in both nominative and accusative singular.

That is why the case difference is shown mainly by η / τη here.

Greek word order is fairly flexible.

The neutral order here is:

• Έχω μια απορία για αυτή τη λέξη.

But other orders are possible, for example:

• Για αυτή τη λέξη έχω μια απορία.
• Μια απορία έχω για αυτή τη λέξη.

These can shift emphasis slightly.
The original version is the most straightforward and natural if you are simply stating the idea.

A simple pronunciation guide is:

EHO mia aporía ya aftí ti léxi

A few helpful points:

• χ in έχω is not like English h exactly; it is a rougher sound, similar to the ch in German Bach or Scottish loch
• για sounds like ya
• αυτή sounds roughly like aftí
• λέξη sounds roughly like LÉK-see

The stress falls on:

• Έχω
• απορία
• αυτή
• λέξη

Yes, absolutely.

That would mean:

• I have a question about this word

The difference is mainly nuance:

• απορία = something I am unsure or puzzled about
• ερώτηση = a question

So both are correct, but απορία can sound a little more like I’m confused about something here.