Learn Hardcore Chinese: qǐng nǐ gàosu wǒ, tā zài nǎr.

Because the main clause is a polite request: 请你告诉我 “please tell me.” The part after the comma, 她在哪儿, is the content you want told. The overall sentence is an imperative/request, so it ends with a period: 。 The comma simply marks a pause; you can also write it without the comma: 请你告诉我她在哪儿。 If you want a question mark, rephrase the whole thing as a yes–no question, e.g. 你能告诉我她在哪儿吗？

Can I drop 你 or replace it with 您?

Yes. All are correct, with slightly different tones of politeness:

请告诉我，她在哪儿。 (neutral, concise)
请你告诉我，她在哪儿。 (polite, but can sound a bit directive)
请您告诉我，她在哪儿。 (more respectful/formal)

Why use 在 instead of 是? Why not say 她是哪儿?

Location in Chinese uses 在 (“to be at/in”). So “Where is she?” is 她在哪儿？/ 她在哪里？ Using 是 would be wrong here: 她是哪儿？ means something like “Which (one) is she?” not a location question.

Where does the question word go? Why “她在哪儿” and not “在哪儿她”?

In Mandarin, question words usually stay in place (in-situ) instead of moving to the front. So you use the normal statement order and put the wh-word where the answer would go: 她在（哪儿） just like 她在（学校）.

Do I add 吗 when using 哪儿? Is “她在哪儿吗？” correct?

Don’t add 吗 to a wh-question. 她在哪儿吗？ is incorrect. You can, however, put 吗 on an outer yes–no question: 你能告诉我她在哪儿吗？ (Can you tell me where she is?)

What’s the difference between 哪儿, 哪里, and 哪?

哪儿 (nǎr) and 哪里 (nǎlǐ) both mean “where.” 哪儿 is common in northern Mainland speech; 哪里 is common nationwide and in Taiwan.
哪 is an informal short form seen in speech/texting: 她在哪？ All three are understood; pick based on region/register.

How do I pronounce everything naturally? Any tone sandhi to watch?

请你: both are 3rd tone, so 3–3 sandhi → pronounce as 2–3: qíng nǐ.
告诉: standard is gào sù (both 4th tone). In fast speech the second syllable may be reduced, but keep it 4th in careful speech.
在: zài (4th).
哪儿: nǎr (3rd tone with r-coloring). The 儿 (r) is not a separate syllable; it merges into the vowel.

Is “请你” the most natural way to be polite? What are alternatives?

It’s correct, but in daily conversation Chinese often prefers softer, indirect wording:

请问，她在哪儿？ (Excuse me, where is she?)
麻烦你告诉我她在哪儿。 (Could I trouble you to tell me where she is?)
你能/可以告诉我她在哪儿吗？ (Could you tell me where she is?) Use 请你… when you want a clear, courteous instruction.

How does 告诉 differ from 说?

告诉 focuses on “tell (someone) something” and takes the recipient directly: 告诉 + 人 + 内容. Example: 请告诉我她在哪儿。
说 is “say/speak.” If you include a listener, use 对/跟 + 人 + 说: 请跟我说她在哪儿。 With just content you can say: 他说她在公司。
For formal writing, 告知 can replace 告诉.

Where do I put 我 in relation to the content? Can I use 把?

With 告诉, the usual order is: 告诉 + 我 +（她在哪儿）. You can also say: 把 + 名词性内容 + 告诉 + 我, e.g. 把她的地址告诉我. But using 把 with a full wh-clause like 把她在哪儿告诉我 is awkward; stick to 告诉我她在哪儿.

Can I just ask directly without “tell me,” e.g., 请问，她在哪儿？

Yes, and that’s often more natural with strangers. 请问，她在哪儿？ directly asks for the location. The original sentence is a polite request for information via “tell me.”

What’s the difference between 哪儿 (nǎr) and 那儿 (nàr)?

哪儿 (nǎr) = where/which place (question word)
那儿 (nàr) = there (that place)
They differ by tone and vowel quality. Don’t mix them up.

Is adding 一下 after 告诉 a good way to sound polite?

With 告诉, 一下 is not the most idiomatic. You’ll hear 告诉我一下, but many prefer:

跟我说一下 (say/tell me briefly)
告诉我一声 (let me know / give me a heads-up)
Or use modal softeners: 你能告诉我…吗？ / 麻烦你告诉我…

Why is 她 (she) pronounced the same as 他 (he) and 它 (it)? How do people tell them apart?

All are pronounced tā. In speech, context tells you which “tā” is meant. In writing, the characters disambiguate: 她 (female), 他 (male), 它 (thing/animal).

Can I add 呢 after 她在哪儿 inside this sentence?

Not in this embedded form. 呢 is a sentence-final particle for direct questions like 她在哪儿呢？ In the request 请你告诉我她在哪儿, you usually leave off 呢 because the clause is content, not a standalone question.

Is “她在不在…？” related to this pattern?

Different function. 她在不在这儿？ is a yes–no question (“Is she here or not?”). 她在哪儿？ asks for a specific location (“Where is she?”). In your sentence, you need the wh-form with 哪儿/哪里.

Does 在 ever mean “be doing” here?

No. 在 can mark progressive aspect when placed before a verb (e.g., 她在吃饭 = she is eating). Here it’s the location verb/preposition “to be at/in”: 她在＋地方.