Na stolu je bila zdjela puna kestena iz parka.

Because na can take different cases depending on the meaning:

• na + accusative = movement onto something
  
  • Stavila je zdjelu na stol. = She put the bowl onto the table.
• na + locative = location on something
  
  • Zdjela je na stolu. = The bowl is on the table.

In your sentence, the bowl is already located there, so Croatian uses the locative: stolu.

Je bila forms the past tense of biti (to be).

Croatian past tense is usually made with:

• a present-tense auxiliary from biti
• plus a past participle

Here:

• je = auxiliary, 3rd person singular
• bila = past participle, feminine singular

So je bila means was.

Because the participle agrees with the subject, and the subject is zdjela (bowl), which is feminine singular.

So:

• masculine singular: bio
• feminine singular: bila
• neuter singular: bilo

Since zdjela is feminine, Croatian says bila.

Croatian word order is more flexible than English word order.

Starting with Na stolu puts the location first, which often sounds natural when introducing a scene:

• Na stolu je bila zdjela puna kestena iz parka.

This is similar to English:

• On the table there was a bowl full of chestnuts from the park.

You could also say:

• Zdjela puna kestena iz parka bila je na stolu.

That is grammatically correct, but it gives a different emphasis. The original version sounds more like setting the scene.

Because the adjective pun / puna / puno (full) normally requires the genitive case for the thing that fills something.

So Croatian says:

• pun vode = full of water
• puna knjiga would be wrong for full of books
• puna knjiga means something else or sounds ungrammatical in this pattern
• correct: puna knjiga is not the right structure; it should be puna knjiga only if knjiga were nominative for another reason, but after puna you want genitive plural: puna knjiga is not acceptable here, and the correct form is puna knjiga? No—better example:
• puna knjiga is wrong
• puna knjiga should be puna knjiga? To avoid confusion:
  
  • puna jabuka = wrong
  • puna jabuka should be puna jabuka? Again confusing because genitive plural equals nominative in some nouns.

For your sentence, the important pattern is:

• puna kestena = full of chestnuts

Here kestena is genitive plural.

Kestena is the genitive plural of kesten (chestnut).

Basic forms:

• singular nominative: kesten
• plural nominative: kesteni
• plural genitive: kestena

It appears here because puna requires the genitive:

• puna kestena = full of chestnuts

In normal interpretation, iz parka most naturally refers to kestena:

• chestnuts from the park

So the whole phrase means:

• a bowl full of chestnuts from the park

Grammatically, Croatian can sometimes allow ambiguity like English does, but context and common sense make the intended meaning clear here. A bowl from the park is possible in theory, but much less likely.

Because iz always takes the genitive case.

So:

• park = nominative
• iz parka = from the park

This is a very useful rule:

• iz kuće = from the house
• iz grada = from the city
• iz parka = from the park

Croatian does not have articles like English a and the.

So zdjela can mean:

• a bowl
• the bowl

The exact meaning depends on context.

That is why Na stolu je bila zdjela puna kestena iz parka can be translated as either:

• There was a bowl full of chestnuts from the park on the table
• On the table was the bowl full of chestnuts from the park

Usually context tells you which is more natural.

Yes, but it is not exactly the same structure.

Compare:

• zdjela puna kestena = a bowl full of chestnuts
• puna zdjela kestena = a full bowl of chestnuts

Both are possible, but the emphasis is slightly different.

• zdjela puna kestena describes the bowl with a following adjective phrase
• puna zdjela kestena treats puna more directly as describing zdjela from the start

In many contexts they are very close in meaning.

Yes, that is possible, but Na stolu je bila... is the more neutral and common order.

Croatian often places the auxiliary je near the beginning of the clause, usually in second position. That is why:

• Na stolu je bila zdjela...

sounds especially natural.

Other word orders may be used for style, emphasis, or rhythm, but a learner should treat Na stolu je bila... as the safest standard pattern.