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You can use she, if you pause to make the meaning clear:

Who is she, playing the piano?

Without the pause, this is a kind of "garden path" sentence, because it leads you to a wrong expectation about how the sentence will end, creating a cognitive dissonance.

Once you hear "who is she playing..." you expect the sentence to end with something like "at tennis on Tuesday?", and the question to be about who she is playing against, rather than who she is to begin with.

Edit

As mentioned in comments, a more common way to express this in everyday speech would be

Who is that playing the piano?

However, I don't believe it would be fair to mark a student wrong for using she.

Personal pronouns don't want to be directly modified, especially in the subjective case.

We naturally say things like "That tall girl is in my class" and "The girl playing piano is very good". Nouns like "girl" work well with adjectives and participial phrases.

We don't naturally say things like "That tall she is in my class" or "She playing piano is very good". The pronoun "she" acts more like a complete and finished noun phrase than a simple noun. It doesn't play nicely with things like adjectives and participial phrases.

How would I explain, in a very simple way, why you cannot use she here?

You can use she but the meaning will be different.

1. Who is he fighting?
   
   Who [is the person] he is fighting against?




2. Who is she talking to?
   
   Who [is the person or people] she is talking to?




3. Who are they going to compete with?
   
   Who [is the person or people] they are going to compete with?




4. Who is she playing the piano? (odd sounding)
   
   To fix this question you need a preposition.

a) Who is she playing the piano with?

b) With whom is she playing the piano? (very formal and rarely heard in speech)

c) Who is she playing the piano to?

d) To whom is she playing the piano?

Sentences b and d are a very formal way of asking a question and rarely heard or used in speech today but by some prescriptivists, it is considered to be the only grammatically correct structure.

I would explain it very simply: a pronoun is supposed to refer clearly to a noun, usually one that precedes the pronoun. The meaning of "pronoun" is something that takes the place of a noun.

An interrogative pronoun will normally not be preceded by a noun because of the way questions are formed in English, but the expectation is that the noun being referred to will follow the pronoun quickly. In the sentence recommended against, there is no noun at all for either "she" or "who."

Thus, the sentence is awkward and not highly idiomatic. I do not think it is ungrammatical, but it is hard to follow. It still would be a bit odd, but much clearer to say "Who is she that is playing the piano." Now the entire clause will be heard as a substitute for a specific noun.

I parse this as similar to:

Who does she think she is, playing the piano?

or

Who is she, to be playing the piano?

The original phrase suggests to me that the piano player is in some way out of place, and the emphasis is not just on the identity of the she, but more on something less pleasant. Depending on the context of the phrase, it may be intended as discriminatory, or it may accidentally reflect a phrasing which has been used to discriminate in the past. Obviously in the context asked it is accidental, but that doesn't capture potential confusion if this sort of phrase is used in conversation.

The answers by The Photon and Gary Potnovcan explain it well, in my opinion, but I'd like to include and addendum focusing on the fact that you're teaching Japanese students.

English pronouns versus Japanese "pronouns"

Let me start quoting Wikipedia:

In linguistics, generativists and other structuralists suggest that the Japanese language does not have pronouns as such, since, unlike pronouns in most other languages that have them, these words are syntactically and morphologically identical to nouns.

So first of all, the confusion of the students is completely understandable because in Japanese the "pronouns" work exactly as nouns. The word the students were probably thinking of is 彼女 (kanojo), which is often translated as "she", but can simply mean "the woman" (excluding the speaker and the person being spoken to). In other words, 彼女 can literally be translated as "the girl" as well.

That said, I believe that, from a teaching perspective, this is a great opportunity to insist on the differences between English pronouns and Japanese "pronouns". Context is a very strong thing in Japanese, almost everything can be omitted and context will do its work. English on the other hand is not: for example, every English clause must have a subject. When there isn't a useful one, we put an "it" there. This is very odd for japanese English learners.

So, what exactly is a pronoun? I am not a linguist, but I'll try: "a pronoun is a word that refers to some other noun that was mentioned before, or is about to be mentioned, or can be inferred by context". If this is not strictly correct, recall that beginners are being taught here so minor nitpicks can be postponed.

In Japanese, we don't use anything like the above definition of pronoun, context itself works already. But in English, we need a word. English sentences have structures much more "solid". Instead of simply omitting everything that can be inferred, as is done in Japanese, in English those things are replaced by pronouns.

So, if we wanted to ask

Who is the girl that I am pointing to right now?

In Japanese we can let context do its work by asking

誰？(dare?)

which is literally just "who?", while in English we need to follow the structural boilerplate which requires a verb and at least a pronoun:

Who is she?

and here "she" is the word that carries the context inside it.

Hopefully this will help clearing things up with the students that might be thinking that she and the girl are exactly the same thing.

I don't know if this will help your students, but here goes. From the formal linguistics perspective, the intended question is constructed by starting with

play piano

Then you attach the interrogative pronoun 'who' as the subject

who play piano

So there's no place for another subject pronoun.

When you make it present tense and imperfective aspect, the verb structure becomes

be who playing piano

The subject 'who' raises to subject position and triggers agreement with 'be' to form

who is playing piano

It's possible that your students are misunderstanding 'who' as a complementizer instead of a pronoun. So in their incorrect sentence 'who is she playing the piano' the 'who' might be intended to correspond to 'whether' in

I wonder whether she is playing the piano

Theoretically, there's a wh-complementizer at the very top of the correct question structure, but it has no spoken content in English. It's similar to 'that' that can be left out here:

I think that she is playing the piano

I think she is playing the piano

Another possibility is that the students are attempting to form

Who is she that is playing the piano

and are trying to use a null complementizer instead of 'that' which isn't allowed in English here. As in, they are forming a phrase parallel to

I like the girl that is playing the piano (but not some other girl)

which you can rephrase without the 'that is'

I like the girl playing the piano (but not some other girl)

The students may also be simply misunderstanding the prompt: Are they supposed to ask a question about the girl's identity, or what she's doing?

Incidentally, questions in English are especially weird when they involve the subject, so I'm not surprised to see ESL students struggling with them. Among other weirdness, they don't trigger do-support:

*Who does be playing the piano

When you are asking about identity, it is a good idea to give the category of person,
- student
- teacher
- man, woman, child
- person
- your friend, their friend etc.

Who is she? [she is not identified at all]. She is my friend and a nice person.
Who is your friend playing the piano?
Who is that person playing the piano?
Who is that playing the piano? [that=that person]

That's the easiest answer I can come up with.

"Who is" introduces a question. It may be followed by:
- a noun: Who is John? Who is that man? Who is the winner?
- an adjective: Who is late?
- a verb: Who is coming to the party. [John is coming to the party.] Who plays the piano?
The pronoun "who" is a subject pronoun in the question "who is [plus verb or noun]", ergo, saying she is ungrammatical. You can't have "who" as an interrogative pronoun and she as a subject pronoun together.

Please note:
Who is playing the piano? Mary is playing the piano.
In the interrogative form, you do not use a pronoun when the identity is unknown.

• 
  Who is playing the piano? Mary is playing the piano.
  versus


• Who is Mary? She is a pianist.


• Who is she? She is Mary.

In the interrogative form, there is no **she (pronoun) because the pronoun here, the subject pronoun is "who".** Therefore, "Who is she playing the piano?" would be providing two subject pronouns.

I think it's because a participle (such as playing the piano) can't modify a personal pronoun (such as she).

These are all correct:

• Who are you looking at? The girl playing the piano.


• Who is the girl playing the piano?


• The girl playing the piano is Sarah.

These are all incorrect:

• Who are you looking at? Her playing the piano.


• Who is she playing the piano?


• She playing the piano is Sarah.

My reason is:

• add a "she" in there, that's to much extra stuff

It would be a valid sentence if you say:

Who is playing the piano?

So i would expect the closest valid sentence to you invalid sentence to be:

Who is the women playing the piano?

Since "she", that could be good with:

Who is she?

But if you merge it with:

Who is playing the piano?

It wouldn't be valid, too many wordings in the sentence.