Η φίλη μου κρατάει σε μια μολυβοθήκη τα μολύβια, το ψαλίδι και τα αυτοκόλλητα του παιδιού.

Yes. μου means my here.

So:

• η φίλη = the friend (feminine)
• μου = my

Together, η φίλη μου means my friend.

In Greek, possessive words like μου, σου, του, της usually come after the noun:

• η φίλη μου = my friend
• το βιβλίο μου = my book

Also, Greek normally keeps the article:

• η φίλη μου, not just φίλη μου in a neutral sentence

Because φίλη is the feminine form, while φίλος is the masculine form.

• ο φίλος μου = my male friend
• η φίλη μου = my female friend

The article changes too:

• ο for masculine
• η for feminine
• το for neuter

Literally, κρατάει often means holds, but in this sentence it is better understood as keeps or stores.

So here:

• Η φίλη μου κρατάει ... τα μολύβια...
  = My friend keeps/stores the pencils...

Greek κρατάω / κρατώ can have several related meanings, such as:

• hold
• keep
• maintain
• retain

In this sentence, because the things are in a pencil case, keeps is the most natural English meaning.

Both are possible in Modern Greek.

• κρατάει
• κρατά

These are two common present-tense forms of the same verb in the 3rd person singular:

• η φίλη μου κρατάει
• η φίλη μου κρατά

Both mean my friend keeps/holds.

The -άει form is very common in everyday language.

Here σε means in.

So:

• σε μια μολυβοθήκη = in a pencil case / in a pencil holder

The preposition σε is very common and can mean different things depending on context, including:

• in
• at
• to
• into
• sometimes on

Here the location makes it clear that it means in.

Because μολυβοθήκη is a feminine noun.

The indefinite articles are:

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

So:

• μια μολυβοθήκη = a pencil case / a pencil holder

If the noun were neuter, you would use ένα instead.

μολυβοθήκη is a noun meaning something like:

• pencil case
• pencil holder
• container for pencils

The exact English translation depends on context.

It is a compound word built from:

• μολύβι = pencil
• θήκη = case / holder / container

So μολυβοθήκη literally suggests a holder/case for pencils.

Greek uses the definite article much more often than English.

So Greek naturally says:

• τα μολύβια
• το ψαλίδι
• τα αυτοκόλλητα

Even where English might leave the article out.

This is very normal in Greek. In a list, each noun often keeps its own article, especially when the speaker means specific items.

So the Greek structure is natural, even if English sounds more natural without repeating the every time.

Because Greek treats ψαλίδι as a singular neuter noun.

• το ψαλίδι = the scissors

This is one of those cases where Greek and English organize the idea differently.

So even though English says:

• the scissors are

Greek says:

• το ψαλίδι είναι
  literally the scissors is

This is completely normal in Greek.

Because Greek uses the genitive case to show possession.

• το παιδί = the child (nominative)
• του παιδιού = of the child / the child’s (genitive)

So:

• τα αυτοκόλλητα του παιδιού = the child’s stickers / the stickers of the child

This is a very common Greek pattern:

• το βιβλίο του μαθητή = the student’s book
• η τσάντα της Μαρίας = Maria’s bag

Grammatically and naturally, it most likely describes only the nearest noun, τα αυτοκόλλητα.

So the most natural reading is:

• the pencils
• the scissors
• and the child’s stickers

In other words, it probably means:

• the pencils
• the scissors
• the stickers belonging to the child

Not necessarily that all three things belong to the child.

If the speaker wanted to make it clearer that the whole set belonged to the child, they would usually phrase it differently.

Yes, Greek word order is fairly flexible.

This sentence is perfectly natural, but you could also say:

• Η φίλη μου κρατάει τα μολύβια, το ψαλίδι και τα αυτοκόλλητα του παιδιού σε μια μολυβοθήκη.

That may sound closer to English word order.

Greek often moves parts of the sentence around for:

• emphasis
• rhythm
• style
• focus

So both orders are possible. The given version puts early attention on where the items are kept: in a pencil case.

The singular is:

• το μολύβι = the pencil

The plural is:

• τα μολύβια = the pencils

This is a common neuter pattern:

• singular in -ι
• plural in -ια

For example:

• το σπίτι → τα σπίτια
• το παιχνίδι → τα παιχνίδια
• το μολύβι → τα μολύβια

The singular is:

• το αυτοκόλλητο = the sticker

The plural is:

• τα αυτοκόλλητα = the stickers

This is another common neuter pattern:

• singular -ο
• plural -α

So:

• το αυτοκόλλητο
• τα αυτοκόλλητα

By default, the present tense κρατάει can mean either:

• something happening right now
• something someone usually does

So the sentence could mean:

• My friend is keeping ... in a pencil case
• or My friend keeps ... in a pencil case

Without more context, Greek allows both readings. Very often, English chooses keeps here because it sounds like a regular arrangement or habit.