genkina kodomotati ga kouen ni imasu.

Because 元気 is a na-adjective in Japanese.

When a na-adjective directly modifies a noun, you add な:

• 元気な子供たち = energetic / healthy children

By itself, 元気 can still function as an adjective-like word:

• 子供たちは元気です = The children are energetic.

So:

• before a noun: 元気な
• at the end of a sentence: 元気です / 元気だ

たち is a common way to show a plural group, especially for people.

• 子供 = child / children
• 子供たち = children

Japanese often does not require a plural marker, so 子供 can already mean children if the context makes that clear. Adding たち makes the plurality more explicit.

So:

• 子供が公園にいます = There is a child / There are children in the park.
• 子供たちが公園にいます = There are children in the park.
  (clearly a group of children)

が marks the grammatical subject, and it is very common in existence sentences with います / あります.

This pattern is very common:

• A が B に います = A is in B / There is A in B

So here:

• 元気な子供たち = energetic children
• が = subject marker
• 公園に = in the park
• います = are / exist (for animate beings)

Using が often presents the subject as new information or simply identifies what exists in that place.

Yes, but the nuance changes.

• 元気な子供たちが公園にいます
  This sounds like There are energetic children in the park or introduces the children as information.

• 元気な子供たちは公園にいます
  This sounds more like As for the energetic children, they are in the park.

So が is natural when you are stating that such children are present there.
は is more topical and can sound contrastive depending on context.

Yes, に can mean different things depending on the sentence.

Here, with います, に marks the location where someone or something exists.

So:

• 公園にいます = is/are in the park

In other sentences, に can mark a destination:

• 公園に行きます = go to the park

So the basic meaning of に changes depending on the verb it goes with.

Because います is used for animate beings—people and animals.

• います = to exist / be present (for people, animals)
• あります = to exist / be present (for things, objects, places, etc.)

Since 子供たち are people, you use います.

Compare:

• 子供たちが公園にいます = The children are in the park.
• ベンチが公園にあります = There is a bench in the park.

This is a very common question.

• に marks the place where something exists / is located
• で marks the place where an action happens

Since います is an existence verb, に is used.

• 子供たちが公園にいます = The children are in the park.

But if the children are doing something there, you would usually use で:

• 子供たちが公園で遊んでいます = The children are playing in the park.

So:

• に
  • existence
• で
  • action

It can be understood either way depending on context, but with が and います, it often feels like an existence statement:

• There are energetic children in the park.

If the children are already the topic of conversation, English might translate it as:

• The energetic children are in the park.

Japanese often leaves that kind of definiteness to context, because it does not have words like the and a/an in the same way English does.

The verb usually comes at the end, but Japanese word order is otherwise fairly flexible because particles show each word’s role.

This sentence uses a very standard order:

• 元気な子供たちが公園にいます

But you could also say:

• 公園に元気な子供たちがいます

This is also natural and often very common in existence sentences. It can feel a bit like:

• In the park, there are energetic children.

So the particles matter more than the order, although some orders sound more natural than others.

No. Normal Japanese is usually written without spaces.

So this sentence would normally be written as:

• 元気な子供たちが公園にいます。

Spaces are often added only in teaching materials to make the sentence structure easier to see.

A natural reading is:

• げんきな こどもたち が こうえん に います。

Word-by-word:

• 元気な → げんきな
• 子供たち → こどもたち
• 公園 → こうえん
• います → います

One small note: in modern Japanese, 子ども is also a very common spelling, so you may see:

• 子どもたち

It is read the same way: こどもたち.