I frikvarteret taler børnene om legepladsen og den store gynge.

No. Here it is the preposition i, meaning in / during / at, but it is capitalized because it is the first word of the sentence.

So:

• i = the preposition
• I = the same word at the start of a sentence

This is not the pronoun I meaning you (plural/formal).

Because Danish main clauses usually follow the V2 rule: the finite verb comes in the second position.

Here, I frikvarteret is placed first, so the verb must come next:

• I frikvarteret = first element
• taler = second element
• børnene = subject, after the verb

So:

• I frikvarteret taler børnene ... = correct
• Børnene taler ... = also correct if the subject comes first instead

Because frikvarteret is the definite form: the recess / the break.

In Danish, this often sounds natural when talking about a specific, familiar school break period. So i frikvarteret means something like during recess or at recess.

The noun is:

• et frikvarter = a recess / a break
• frikvarteret = the recess / the break

If you said i et frikvarter, that would mean in a recess / during one recess, which is less general and more specific to one particular instance.

Because barn has an irregular plural.

The forms are:

• et barn = a child
• børn = children
• børnene = the children

So børnene is the definite plural form. You have to learn this one as an irregular pattern.

It marks the definite plural.

So:

• børn = children
• børnene = the children

In this sentence, we are talking about a specific group of children, not just children in general.

Because Danish often puts the definite article at the end of the noun.

So:

• en legeplads = a playground
• legepladsen = the playground

This is very common in Danish. Instead of using a separate word like English the, Danish often adds a definite ending to the noun.

Because when a noun has an adjective before it, Danish normally uses:

• den/det/de
  • adjective + noun in its basic form

So:

• en gynge = a swing
• gyngen = the swing
• den store gynge = the big swing

You do not normally add the definite ending -en to the noun when you already have den plus an adjective in front.

So:

• den store gynge = correct
• den store gyngen = not standard Danish

Because adjectives usually take -e when they come before a definite noun phrase.

Here the phrase is definite because of den:

• en stor gynge = a big swing
• den store gynge = the big swing

So stor becomes store in this structure.

Tale om means to talk about.

So:

• taler om legepladsen = talk about the playground

The preposition om belongs with taler here. It is the normal way to say talk about.

Because one preposition can apply to both nouns when they are joined by og.

So:

• taler om legepladsen og den store gynge

means:

• talk about the playground and the big swing

You could repeat om, but normally you do not need to:

• taler om legepladsen og om den store gynge

That is possible, but less smooth here unless you want extra emphasis.

Yes, very often you can.

• taler is a bit more neutral or slightly more formal
• snakker is more everyday and conversational

So I frikvarteret snakker børnene om legepladsen og den store gynge is also natural Danish.

Yes. That is also correct.

The difference is mainly emphasis and sentence structure:

• I frikvarteret taler børnene ... puts the time first, so during recess is highlighted
• Børnene taler ... i frikvarteret starts with the subject, so it feels a bit more neutral

Both are grammatical.