Learn Hardcore Japanese: kodomotati ha kouen de kenka wo surukoto ga arimasu.

So けんかをすることがあります is literally there are times when (they) do fighting, which is naturally translated as they sometimes fight or they occasionally fight.

This pattern [dictionary-form verb] + ことがある is commonly used to express occasional / sometimes-occurring actions in a neutral, factual way.

Why do we need こと here? Why not just けんかをするがあります?

こと turns the verb phrase けんかをする (to fight) into a noun-like phrase:

けんかをする = to fight (verb phrase)
けんかをすること = the act of fighting / fighting (as a thing)

The verb あります needs a noun as its subject:

本があります。 = There is a book.
問題があります。 = There is a problem.

Similarly:

けんかをすることがあります。
= There are times when fighting happens.
= Sometimes they fight.

You cannot say けんかをするがあります because する is a verb and cannot directly be the subject of あります. You first nominalize it with こと.

What is the difference between けんかをする and けんかする?

Both mean to fight / to quarrel and are both correct.

けんかをする: uses を explicitly; feels a bit more careful / full form.
けんかする: drops を; slightly more casual or natural in fast speech.

In most contexts, they are interchangeable in meaning:

子供たちは公園でけんかをする。
子供たちは公園でけんかする。

Both: Children fight in the park.

In the given sentence, you could also say:

子供たちは公園でけんかすることがあります。

No real change in meaning.

Why is 公園 followed by で and not に?

で marks the place where an action happens.

公園でけんかをする = to fight in the park (the park is the place where the action occurs).

に after a place usually marks:

destination / goal: 学校に行く (go to school)
existence / location of being: 公園に子供がいる (there are children in the park)

But for actions performed at a place, Japanese normally uses で:

公園で遊ぶ = play in the park
公園で走る = run in the park
公園でけんかをする = fight in the park

So 公園で is the correct choice here.

Why is 子供たち followed by は and not が?

は marks the topic; が marks the subject (grammatically focused doer).

In this sentence, we are talking about children as a general topic:

子供たちは… = As for children, / Speaking about children, …

Then the statement about them is:

公園でけんかをすることがあります。
= there are times when they fight in the park.

If you used が:

子供たちが公園でけんかをすることがあります。

this sounds more like you are introducing or emphasizing that it is specifically the children who sometimes fight (for example, in contrast to adults). It is possible, but は is more natural here for a general statement about children.

Why do we use あります and not します (for example けんかをします)?

There are two different patterns here:

Direct action:
- 子供たちは公園でけんかをします。
  = Children fight in the park.
  This simply states a habitual action (they fight there, generally).
There-are-times-when pattern:
- 子供たちは公園でけんかをすることがあります。
  = There are times when children fight in the park.
  = Children sometimes fight in the park.

In the second one, the main verb is あります (there is / exist), and its subject is けんかをすること (the act of fighting). So the structure is:

[fighting] (けんかをすること) + が + [exists sometimes] (あります)

This is why します does not appear: we are not directly saying they fight; we are saying there are some times when they fight.

What is the difference between Vることがある and Vたことがある?

They are different patterns:

Vることがある (dictionary form + ことがある)
- Expresses sometimes / occasionally happens.
- Example:
  - 子供たちは公園でけんかをすることがあります。
    = Children sometimes fight in the park.
Vたことがある (past form + ことがある)
- Expresses experience: have done something before.
- Example:
  - 公園でけんかをしたことがあります。
    = I have fought in a park before. / I have had the experience of fighting in a park.

So:

することがある → sometimes do
したことがある → have done (at least once in the past)

Is 子供たち definitely plural? How does plurality work here?

子供たち is clearly plural: たち is a plural-like suffix, so 子供たち is children.

However, Japanese often does not need plural markers. You could also say:

子供は公園でけんかをすることがあります。

This can still be understood as children sometimes fight in the park, especially in a general statement. The は here would usually be interpreted as children in general.

Using 子供たち just makes the plurality explicit and feels a bit more concrete (we are thinking of multiple kids rather than the abstract category child).

What tense is あります here? Does the sentence talk about the present or the future?

あります is the non-past polite form. In Japanese, non-past covers both present and future.

In this pattern Vることがあります, it generally means:

A general truth or habit across time:
There are (sometimes) such occasions.

So the sentence means in general, at times, children fight in the park. It is not tied to a specific moment; it expresses a general, recurring possibility.

Could we just say 子供たちは公園でけんかします instead? What is the difference?

Yes, you can say:

子供たちは公園でけんかします。
= Children fight in the park.

Difference in nuance:

子供たちは公園でけんかします。
→ Sounds like a regular habit / fact. It can be heard as they (often / usually) fight there, depending on context.
子供たちは公園でけんかをすることがあります。
→ Clearly emphasizes sometimes / occasionally.
It sounds softer, less absolute: There are times when they fight in the park.

So the ことがあります version is good when you specifically want sometimes, not always or regularly.

Is this sentence polite or casual? How would a casual version look?

The given sentence is in polite form because of あります.

A more casual version might be:

子供たちは公園でけんかすることがある。
Or even shorter in speech: 子供って公園でけんかすることあるよ。

Changes:

あります → ある (plain form)
Possible substitution of 子供たちは with 子供って in casual speech, where って is a casual topic marker.

Meaning stays the same, but politeness level drops.

Why is けんか written in hiragana here? Is there a kanji form and any nuance?

けんか can be written in:

けんか (hiragana)
ケンカ (katakana)
喧嘩 (kanji)

All mean fight / quarrel.

In modern writing, especially for learners and in everyday texts, hiragana is very common because 喧嘩 uses less common, visually complex kanji.

There is usually no strong change in meaning:

喧嘩をする = けんかをする = to fight / quarrel.

Katakana ケンカ can sometimes feel a bit more casual or emphatic, but context matters more than script choice here.