Το σεντούκι είναι δίπλα στο κρεβατάκι και μέσα έχει άλλο ένα παιχνιδάκι και ένα βιβλίο.

Yes, Greek uses the definite article very often, more often than English does.

• το = the for a neuter singular noun
• σεντούκι = chest / trunk

So Το σεντούκι means the chest.

In Greek, leaving out the article here would usually sound unnatural unless you were speaking in a very special context, like labels, dictionary entries, or very reduced note-style language.

σεντούκι means a chest, trunk, or storage box, usually something like a wooden box with a lid.

It is a neuter noun, which is why it takes neuter words like:

• το σεντούκι
• ένα σεντούκι

Because στο is the normal contracted form of σε το.

• σε = at / to / in / on, depending on context
• το = the for neuter singular
• σε το → στο

So:

• δίπλα στο κρεβατάκι = next to the little bed

This contraction is standard and very common:

• σε + το = στο
• σε + τη(ν) = στη(ν)
• σε + τα = στα

δίπλα means next to or beside.

In this sentence, it is followed by στο κρεβατάκι, so the whole phrase means:

• δίπλα στο κρεβατάκι = next to the little bed

You can think of δίπλα as expressing position. Very often it appears with σε + noun:

• δίπλα σε ένα τραπέζι = next to a table
• δίπλα στο κρεβατάκι = next to the little bed

The ending -άκι is a very common diminutive ending in Greek. It often gives the idea of:

• small size
• affection
• cuteness
• something child-related

So:

• κρεβάτι = bed
• κρεβατάκι = little bed / small bed

and:

• παιχνίδι = toy / game
• παιχνιδάκι = little toy / small toy

In children’s contexts, -άκι is especially common.

It is in the accusative, because σε normally takes the accusative in Modern Greek.

So underneath στο κρεβατάκι, the structure is:

• σε
  • το κρεβατάκι

The reason it may not look different to you is that many neuter nouns have the same form in the nominative and accusative singular.

So:

• nominative: το κρεβατάκι
• accusative: το κρεβατάκι

Same form, different grammatical role.

Here μέσα is an adverb, meaning inside.

So in:

• και μέσα έχει...

it means something like:

• and inside it has...
• more naturally in English: and inside there is... or and inside it contains...

μέσα can also appear in other structures, but here it is simply telling you where the following things are: inside the chest.

Because Greek often omits subject pronouns when they are understood from context.

Here, the understood subject of έχει is the chest:

• Το σεντούκι είναι δίπλα στο κρεβατάκι και μέσα έχει...
• literally: The chest is next to the little bed and inside has...
• natural English: The chest is next to the little bed and inside it has... / and inside there is...

This kind of omission is very normal in Greek. The speaker does not need to repeat it because the chest is already the topic.

Yes, έχει is the 3rd person singular of έχω = to have.

• έχω = I have
• έχεις = you have
• έχει = he/she/it has

So μέσα έχει άλλο ένα παιχνιδάκι και ένα βιβλίο literally means:

• inside it has another little toy and a book

In English, depending on style, you might also translate it more naturally as:

• inside there is another little toy and a book
• it contains another little toy and a book

άλλο ένα means another one or one more.

In this sentence:

• άλλο ένα παιχνιδάκι = another little toy / one more little toy

The word άλλο agrees with the noun it goes with. Since παιχνιδάκι is neuter singular, you get άλλο.

Compare:

• άλλος φίλος = another friend (masculine)
• άλλη φίλη = another friend (feminine)
• άλλο παιχνίδι = another toy/game (neuter)

Because άλλο ένα only belongs to παιχνιδάκι.

So the structure is:

• άλλο ένα παιχνιδάκι = another little toy
• και ένα βιβλίο = and a book

It does not mean another little toy and another book. It means:

• one more little toy
• plus
• a book

If the speaker wanted to say another book too, they would need to say that explicitly.

Yes, Greek word order is fairly flexible.

The sentence puts μέσα early to highlight location first:

• και μέσα έχει... = and inside it has...

Other possible ways to say something similar could be:

• και έχει μέσα...
• και μέσα στο σεντούκι έχει...
• και στο εσωτερικό του έχει... (more formal/literary)

The version in your sentence sounds natural and simple, especially in descriptive language.

Because neither of those words is a noun here.

• μέσα is an adverb: inside
• άλλο is a determiner/adjective-like word modifying ένα παιχνιδάκι

Articles like το, η, ο, ένα, μια go with nouns, not with adverbs like μέσα.

So:

• μέσα = no article
• άλλο ένα παιχνιδάκι = άλλο modifies the noun phrase, but ένα is the actual indefinite article

It sounds neutral to mildly colloquial, and very natural in everyday descriptive speech, especially in a child-related context because of the diminutives:

• κρεβατάκι
• παιχνιδάκι

Also, the phrasing μέσα έχει... is common and natural in ordinary speech. A more formal version might phrase things differently, but this sentence is perfectly normal conversational Greek.