Η ανιψιά μου με ρωτάει πώς κινείται κάθε πιόνι σε κάθε επιτραπέζιο παιχνίδι.

In Greek, a possessive (like μου, “my”) almost always comes together with the definite article.

• Η ανιψιά μου = literally “the niece of mine”, i.e. my niece.
• Saying just ανιψιά μου is possible, but it sounds more emotional/poetic/intimate or like a form of address:
  
  • Ανιψιά μου, έλα εδώ! – My niece, come here!

In normal, neutral statements, the article η is expected: Η ανιψιά μου μένει κοντά. – My niece lives nearby.

They are two different pronouns:

• μου = “my” / “of me” (genitive, possessive)
  • Η ανιψιά μου = my niece
• με = “me” (accusative, direct object)
  • με ρωτάει = she asks me

So the structure is:

• Η ανιψιά μου – subject: my niece
• με – object: me
• ρωτάει – verb: asks

Literally: “My niece me asks …” – which in English is “My niece asks me …”.

Clitic object pronouns like με, σε, τον, τη, μας, σας, τους normally go before the verb in simple statements:

• Με ρωτάει. – She asks me.
• Τον βλέπω. – I see him.
• Σας ακούω. – I hear you.

Putting με after the verb (ρωτάει με) is incorrect in this structure.

You can put a stressed form εμένα after the verb for emphasis:

• Η ανιψιά μου ρωτάει εμένα. – It’s me that my niece asks (emphasis on me).

But the normal, unstressed object is με before the verb: με ρωτάει.

Yes, both are correct present-tense 3rd-person singular forms of ρωτάω / ρωτώ (to ask).

• ρωτάει – more colloquial/spoken
• ρωτά – slightly shorter, a bit more formal or written

They mean the same:

• Η ανιψιά μου με ρωτάει …
• Η ανιψιά μου με ρωτά …

Both: My niece asks me …

Modern Greek present tense can cover all of these, depending on context:

• Simple present: asks me (general statement or habit)
• Present continuous: is asking me (right now)
• Habitual: keeps asking me / often asks me

In your sentence, without extra adverbs like συχνά (often) or τώρα (now), the default reading is a general/habitual situation: My niece (typically / regularly) asks me…
But grammatically, it is just present tense; the exact nuance comes from context.

The verb comes from:

• Active: κινώ / κινάω – to move (something)
• Middle/passive: κινούμαι – to move (myself), to be moving

κινείται is 3rd person singular of κινούμαι:

• κινείται = it moves / it is moved / it is in motion

Greek often uses this middle/passive form when an object moves by itself or when we speak about its movement in a general, impersonal way:

• Πώς κινείται κάθε πιόνι; – How does each piece move?
  (Not “how does someone move each piece”, but “how does it move / is supposed to move”.)

If you said πώς κινάει κάθε πιόνι, it would sound more like “how does each piece move (something else)” – which is not what we mean here.

Base / dictionary forms:

• Active: κινώ or κινάω – to move (something)
• Middle/passive: κινούμαι – to move (oneself); to be moving

Present tense (middle/passive) of κινούμαι:

• (εγώ) κινούμαι – I move / am moving
• (εσύ) κινείσαι – you move
• (αυτός/αυτή/αυτό) κινείται – he/she/it moves
• (εμείς) κινούμαστε or κινούμαστε/κινούμεθα – we move
• (εσείς) κινείστε – you (pl.) move
• (αυτοί/αυτές/αυτά) κινούνται – they move

So κινείται fits exactly as “each piece moves”.

κάθε means “each / every” and it always takes a singular noun:

• κάθε παιδί – each/every child
• κάθε μέρα – every day
• κάθε πιόνι – each/every piece (chess/checkers piece, etc.)

Even though in meaning you’re talking about all the pieces, grammatically you use singular with κάθε, just like in English with “every”:

• “Every piece moves like this” → Κάθε πιόνι κινείται έτσι.

σε is a very flexible preposition in Greek. Depending on context, it can mean:

• to (direction): Πηγαίνω σε ένα φίλο. – I’m going to a friend.
• in / inside: Είναι σε ένα κουτί. – It is in a box.
• on / at: Στο τραπέζι, στη δουλειά – on the table, at work.

In σε κάθε επιτραπέζιο παιχνίδι, it’s best translated as “in every board game”:

• Literally: in each board game
• Functionally: σε = “in” here.

Spoken Greek often contracts σε + το, σε + την etc. (e.g. στο παιχνίδι, στην τάξη), but here it’s followed by κάθε, so we use the full σε κάθε form.

επιτραπέζιο παιχνίδι is made of:

• επιτραπέζιο – adjective from τραπέζι (table) → “tabletop / table-”
• παιχνίδι – game

So literally: “tabletop game”, i.e. board game.

In everyday speech, people often shorten it and just say ένα επιτραπέζιο:

• Θες να παίξουμε ένα επιτραπέζιο; – Do you want to play a board game?

Your sentence uses the full phrase επιτραπέζιο παιχνίδι, which is slightly more explicit/formal, but both ways are natural.

With both κάθε’s:

• κάθε πιόνι σε κάθε επιτραπέζιο παιχνίδι
  = each piece in each board game
  (for every board game, and for each piece inside each of those games)

If you drop the second κάθε:

• κάθε πιόνι σε επιτραπέζιο παιχνίδι
  This sounds incomplete and odd in this context; it suggests “each piece in a board game” in a very generic, vague way.

More natural variants:

• κάθε πιόνι σε κάθε επιτραπέζιο παιχνίδι – strong emphasis: every piece in every board game
• κάθε πιόνι σε ένα επιτραπέζιο παιχνίδι – each piece in a board game (sounds like “per game type”)
• Or we can change structure entirely: σε κάθε επιτραπέζιο παιχνίδι, πώς κινείται κάθε πιόνι;

But in your exact sentence, the double κάθε is clear and natural.

These two are different words in Modern Greek:

• πώς (with accent) = how (question word)
  • Πώς κινείται; – How does it move?
• πως (no accent) = that (conjunction, like “that” or sometimes “how” in reported speech)
  • Μου είπε πως θα έρθει. – He told me that he will come.

In your sentence:

• πώς κινείται κάθε πιόνι – how each piece moves → must use πώς with an accent, because it is a question word (even in indirect questions).

Yes:

• ανιψιά – niece (female)
• ανιψιός – nephew (male)

Plurals:

• ανιψιές – nieces
• ανιψιοί – nephews (or mixed group: nieces + nephews)

So:

• Η ανιψιά μου – my niece
• Ο ανιψιός μου – my nephew
• Οι ανιψιοί μου – my nephews / my nieces and nephews

You can, but the meaning changes slightly.

• Η ανιψιά μου με ρωτάει πώς κινείται…
  → My niece asks me how … (I am the person being asked.)
• Η ανιψιά μου ρωτάει πώς κινείται…
  → My niece asks how … (we know she’s asking, but not necessarily whom.)

The second version is possible if the person being asked is either obvious from context or unimportant, but if you want to say clearly that she asks me, you need με.