Hon ropade på barnen från balkongen när maten var klar.

In Swedish, ropa på någon is a common expression meaning call to someone or call for someone.

• ropa by itself = shout / call out
• ropa på barnen = call to the children to get their attention

So på is not literally on here. It belongs to the verb expression.

Compare:

• Hon ropade högt. = She shouted loudly.
• Hon ropade på barnen. = She called to the children.

It is the definite plural ending.

With barn:

• ett barn = a child
• barn = children
• barnen = the children

So barnen is not just children in general, but the children.

Not necessarily. Barnen only means the children.

It can refer to:

• her children
• some children already known in the conversation
• a specific group of children in the situation

Swedish does not mark possession here. If you wanted to say her children explicitly, you would say hennes barn.

Because från means from, and here it shows the source of the calling.

• från balkongen = from the balcony
• på balkongen = on the balcony

Both can be possible in different sentences, but they mean slightly different things:

• Hon ropade på barnen från balkongen. = She called to the children from the balcony.
• Hon var på balkongen. = She was on the balcony.

So in your sentence, från balkongen tells us where her call came from.

Here klar means ready.

The form changes to match the noun:

• Maten var klar. = The food was ready.
• Huset var klart. = The house was ready / finished.
• Barnen var klara. = The children were ready.

Since maten is a singular en-word, the adjective is klar.

Because the whole sentence is in the past.

• ropade = called
• var = was

So the timing is:

• she called to the children
• at that time, the food was ready

If you said är, it would sound like a present-time statement mixed into a past-time sentence, which usually does not fit here.

The basic form is ropa.

This verb is conjugated like this:

• infinitive: ropa = to call / shout
• present: ropar = calls / is calling
• past: ropade = called
• supine: ropat = called

So Hon ropade means She called.

Yes. A very natural alternative is:

När maten var klar ropade hon på barnen från balkongen.

When the sentence starts with the time clause, the main clause changes word order:

• Hon ropade ...
• När maten var klar ropade hon ...

This is the normal verb-second pattern in Swedish: when something comes first, the finite verb comes before the subject in the main clause.

It most naturally describes where she was calling from.

So the usual reading is:

• she was on the balcony
• from there, she called to the children

It does not normally mean that the children were on the balcony.

If you wanted to make the children’s location clearer, Swedish would usually say that more directly.

It is a subordinate time clause introduced by när = when.

Inside that clause, the word order is normal subordinate-clause order:

• när maten var klar

In Swedish subordinate clauses, you do not get the same kind of inversion as in main clauses. Here it is simply:

• maten = subject
• var = verb
• klar = complement

So this part tells us when she called to the children.