Learn Hardcore Japanese: genkina kodomotati ga kouen ni imasu. - There are energetic children in the park.

bold に marks the location of existence (the place), and bold が marks the thing/person that exists there (the subject). This follows the pattern: Place bold に + Thing/Person bold が + bold いる/ある. So the children (subject) exist at the park (location).

Why is bold います used instead of bold あります?

Use bold いる/います for animate beings (people, animals). Use bold ある/あります for inanimate things and abstract items. Children are animate, so bold います is correct.

Can I use bold で instead of bold に?

Not for simple existence. bold に is used with bold いる/ある to state that something/someone exists at a location. bold で marks where an action happens. Compare:

Existence: 公園 bold にいます (at/in the park).
Action: 公園 bold で遊んでいます (playing at the park).

Why does bold 元気 take bold な before bold 子供たち? Isn’t bold 元気 an adjective?

Yes—bold 元気 is a bold な‑adjective. When a bold な‑adjective directly modifies a noun, it takes bold な: bold 元気な子供たち. By contrast, bold い‑adjectives don’t add anything: 楽しい子供. As a predicate you can say 元気です (“(They) are fine/energetic”).

Do I need bold たち to mean “children”? Isn’t plural optional in Japanese?

Plural is generally optional. bold 子供 can mean “child/children” from context. Adding bold たち (bold 子供たち) explicitly emphasizes plurality or a specific group of children. bold たち is mainly used with animate nouns and is not used with most inanimate things.

Is bold 子供 or bold 子ども correct? Which should I use?

Both are common. Many schools and some publications prefer bold 子ども; everyday writing often uses bold 子供. Either is fine—be consistent within the same text.

Why are there spaces between the words here? Do Japanese normally write like this?

The spaces are for learners. Standard Japanese writing doesn’t use spaces between words. You’d normally write: 元気な子供たちが公園にいます。 Reading: げんきなこどもたちがこうえんにいます (romaji: genkina kodomotachi ga kōen ni imasu).

Can I change the order to bold 公園に元気な子供たちがいます?

Yes. In fact, “Place bold に Subject bold がいます” (bold 公園に…がいます) is a very common presentational order: “At the park, there are …”

Can I replace bold が with bold は? What changes?

bold 子供たち bold は公園にいます: “As for the children, they’re at the park.” It presumes we’re already talking about those children or contrasts them with something else.
bold 公園 bold には元気な子供たち bold がいます: “As for the park, there are lively children (there).” For introducing new information (“There are …”), bold が is the default subject marker.

How do I say this casually?

Use the plain form bold いる: 元気な子供たちが公園に bold いる. Polite: bold います; plain: bold いる.

How do I make it negative or past?

Polite: いません (not there), いました (was/were there), いませんでした (wasn’t/weren’t there)
Plain: いない, いた, いなかった Note: When stating “there is none/no …,” Japanese often uses bold は instead of bold が: 公園に子供 bold はいません (“There are no children at the park”).

How do I ask this as a question?

Add bold か: 公園に元気な子供たちがいます bold か. A common way to ask about existence is 公園に子供 bold はいますか (“Are there any children at the park?”). Typical answers: はい、います / いいえ、いません.

How do I say how many children are there?

Use the people counter bold 〜人 (ひとり, ふたり, さんにん, よにん…):

公園に子供 bold が三人います. (“There are three children in the park.”)
三人の子供 bold が公園にいます. Avoid combining a counter with bold たち (e.g., ×三人の子供たち) in neutral counting.

What happens if bold 元気な modifies bold 公園 instead (bold 元気な公園)?

The modifier would switch to the park: “children are in a lively/energetic park.” However, bold 元気 usually describes people/animals, so bold 元気な公園 sounds odd. More natural for a lively park is bold にぎやかな公園 or bold 活気のある公園.

Is bold で + bold いる ever okay?

Not with plain existence. bold で marks where an action/state is happening, so you’ll use it with verbs in bold 〜ている that describe activities: 公園で遊んでいる (“(They) are playing at the park”). Plain bold いる as “to exist/be (somewhere)” uses bold に: 公園にいる.

Are there more polite or honorific versions of bold いる?

Yes:

bold おります: humble polite form of bold いる, used for yourself/your in‑group (e.g., 会場にスタッフがおります).
bold いらっしゃいます: honorific polite form for respected subjects (e.g., お客様がロビーにいらっしゃいます). For a neutral statement about children, bold います is appropriate.