Η ανιψιά μου βρήκε ένα όμορφο κοχύλι και μετά είδε ένα μικρό καβούρι δίπλα στο νερό.

η is the feminine singular definite article, meaning the.

In Greek, my niece is normally expressed as η ανιψιά μου — literally something like the niece my. Greek usually keeps the definite article with possessive expressions like this:

• η αδερφή μου = my sister
• ο φίλος μου = my friend
• το σπίτι μου = my house

So η is not extra; it is the normal Greek way to say it.

Because μου is the usual unstressed possessive form, and in normal Greek it comes after the noun:

• η ανιψιά μου = my niece
• το βιβλίο μου = my book

Putting it before the noun is not the normal pattern in standard everyday Greek.

If you want emphasis, Greek can use stronger forms such as δική μου, but that is a different structure:

• η δική μου ανιψιά = my own niece / my niece, not someone else’s

Greek often drops subject pronouns when they are not needed. The verb form already tells you the subject is he/she/it.

So:

• βρήκε = he/she found
• είδε = he/she saw

Because the subject is already clear from context and from the verb ending, Greek does not need to say αυτή (she) here.

If αυτή were added, it would usually sound emphatic:

• Αυτή βρήκε... = She found... (as opposed to someone else)

They are in the aorist, which is the normal Greek past tense for a completed action.

Here it is used to narrate a sequence of events:

• βρήκε = found
• είδε = saw

This is very common in storytelling and simple past narration.

Also, both verbs are based on present-tense verbs with different stems:

• βρίσκω → βρήκε
• βλέπω → είδε / είδα

So these are forms you usually need to learn as past-tense patterns, not by just changing one ending mechanically.

ένα is the indefinite article for neuter singular nouns — basically a/an.

Both κοχύλι and καβούρι are neuter singular nouns, so they both take ένα:

• ένα κοχύλι = a shell
• ένα καβούρι = a crab

It is used here because these are being introduced as new, non-specific things in the story.

Because Greek adjectives must agree with the noun they describe in:

• gender
• number
• case

Here:

• κοχύλι is neuter singular
• καβούρι is neuter singular

So the adjectives are also in the neuter singular form:

• όμορφος / όμορφη / όμορφο
• μικρός / μικρή / μικρό

That is why the sentence has:

• ένα όμορφο κοχύλι
• ένα μικρό καβούρι

They are objects, so they are in the accusative case. But with many neuter singular nouns, the nominative and accusative forms are identical.

So for neuter nouns, the subject form and object form often look the same.

For example:

• το κοχύλι = the shell (subject)
• βλέπω το κοχύλι = I see the shell (object)

Same with καβούρι.

So yes, they are objects here, but neuter nouns often do not visibly change form.

Together, και μετά means and then.

• και = and
• μετά = then / afterwards

Greek often uses μετά to move the story forward in time. So the sentence first says she found something, and then she saw something else.

You could also hear just μετά in similar contexts:

• Μετά είδε ένα καβούρι. = Then she saw a crab.

It means next to the water / beside the water.

The key parts are:

• δίπλα = next to / beside
• στο = contraction of σε + το
• νερό = water

So:

• δίπλα στο νερό = literally beside at-the water, but naturally next to the water

Greek very often contracts σε + το into στο.

Examples:

• σε το σπίτι → στο σπίτι
• σε το νερό → στο νερό

Because νερό is a neuter noun.

The article must match the noun’s gender:

• masculine: τον → στον
• feminine: τη(ν) → στη(ν)
• neuter: το → στο

Since νερό is neuter, Greek uses:

• το νερό
• στο νερό

If it were a masculine noun, then you might get στον instead.

Greek word order is more flexible than English word order, because the grammar is often shown by endings and articles.

The sentence as written is a very natural, neutral order for narration:

• Η ανιψιά μου βρήκε... και μετά είδε...

But other orders are possible for emphasis, for example:

• Μετά, η ανιψιά μου είδε ένα μικρό καβούρι...
• Ένα μικρό καβούρι είδε μετά η ανιψιά μου...
  This is possible, but much more marked and less neutral.

So yes, Greek can move things around more than English, but the original sentence is the most straightforward version for ordinary storytelling.