kanozyo ni ha nouryoku ga arimasu.

They are doing different jobs.

• に marks the possessor/target/location-like place where something exists.
• は marks that whole part, 彼女に, as the topic.

A very common pattern is:

• X には Y がある = X has Y
  literally: As for X, Y exists (for/in relation to X)

So:

• 彼女には能力があります
• literally: As for her, ability exists
• natural English: She has ability / She is capable

The は can also add a slight contrastive feeling depending on context.

Because with ある / いる, the thing that exists is usually marked by が.

In this sentence, the thing that exists is 能力.

So the structure is:

• 彼女には = as for her / for her
• 能力が = ability exists
• あります = there is / exists

This is why が is natural here.

Because 能力 is an abstract thing, not a living being.

• ある / あります → used for things, including abstract things like time, money, ability, chance, problem
• いる / います → used for people and animals

So:

• 能力があります = there is ability / someone has ability
• not 能力がいます, because ability is not alive

A fairly literal translation is:

• As for her, ability exists

Japanese often expresses having with an existence pattern instead of a special verb like English have.

So even though the literal structure sounds strange in English, it naturally means:

• She has ability
• She is capable

This is the same idea as:

• 私には兄がいます = I have an older brother
• literally: As for me, an older brother exists

は marks 彼女に as the topic, but it can also suggest contrast.

So 彼女には能力があります can sound like:

• She has ability
• She, at least, has ability
• As for her, she does have ability

Whether that contrast is actually felt depends on context.

Without a strong context, it may just sound like normal topicalization. But compared with 彼女に能力があります, the version with は more easily allows a contrastive reading.

Yes, you can, but the nuance changes a little.

• 彼女に能力があります
  more neutral, just stating that she has ability

• 彼女には能力があります
  marks her as the topic and may suggest contrast or emphasis

In many real conversations, には is very common in this pattern.

You may hear it, but 彼女には能力があります is more natural for this specific possession/existence pattern.

Why?

Because the underlying structure is really:

• 彼女に
  • 能力がある

That に is important because it marks the possessor.

So:

• 彼女には能力があります = very natural
• 彼女は能力があります = possible in some contexts, but less standard/natural as an example of this pattern

A more common alternative with は directly after 彼女 would be something like:

• 彼女は能力がある
• 彼女は有能です

No. 彼女 can also mean girlfriend, depending on context.

So this sentence could theoretically mean:

• She has ability
• My girlfriend has ability

But in a basic grammar example like this, it is usually understood as she.

Japanese often depends on context to decide which meaning is intended.

Japanese word order is more flexible than English, but particles show each word’s role.

In this sentence:

• 彼女には = topic/possessor
• 能力が = thing that exists
• あります = verb

A very normal order is:

• topic + subject/existing thing + verb

So:

• 彼女には能力があります

You might see different orders in special contexts, but this is the most straightforward and natural one.

あります is the polite form.

The plain form is:

• ある

So:

• polite: 彼女には能力があります
• plain: 彼女には能力がある

Both mean the same thing. The difference is politeness.

Use:

• あります in polite conversation, class, formal writing
• ある in casual speech, plain statements, dictionaries

Yes. That is another natural way to express a similar idea.

• 彼女には能力があります
  literally based on existence
  natural, common, simple

• 彼女は能力を持っています
  literally she possesses ability
  a bit more direct and sometimes a little more formal or explicit

Both are grammatical, but X には Y がある is a very important basic Japanese pattern, so this sentence is often used to teach that structure.