न तो तुम थकी हो, न ही मैं थकी हूँ।

It is the Hindi equivalent of neither ... nor ....

So:

• न तो तुम थकी हो = you are not tired
• न ही मैं थकी हूँ = nor am I tired

Together, the whole sentence means Neither are you tired, nor am I tired.

The words तो and ही add structure and emphasis. Hindi also often uses simpler versions like न ... न ....

Because थका / थकी / थके changes to match gender and sometimes number.

Here, थकी is the feminine form, so the sentence is being said with feminine agreement:

• तुम थकी हो = said to a female addressee
• मैं थकी हूँ = said by a female speaker

So this sentence strongly suggests that the speaker is female, and the person being addressed is also female.

Because Hindi uses different present-tense forms of होना depending on the subject.

Relevant forms here are:

• मैं हूँ = I am
• तुम हो = you are

So:

• तुम थकी हो
• मैं थकी हूँ

Those are the normal combinations.

In this sentence, ही mainly adds emphasis and helps complete the neither ... nor ... structure.

It does not always need a separate English translation. You can think of it as reinforcing the second half:

• न तो ...
• न ही ...

So ही is not the main negative word here; it just strengthens the expression.

Because Hindi usually uses न in paired negative structures like neither ... nor ....

So this is natural:

• न तो तुम थकी हो, न ही मैं थकी हूँ।

But with ordinary single negation, you would usually use नहीं:

• तुम थकी नहीं हो।
• मैं थकी नहीं हूँ।

So both न and नहीं can negate, but they are used in different kinds of structures.

Hindi commonly repeats it so that each clause is complete:

• न तो तुम थकी हो
• न ही मैं थकी हूँ

That is clearer and more standard.

In casual speech, people may sometimes leave out repeated words if the meaning is obvious, but for learners, it is best to understand the full form first.

It can be either, depending on context.

तुम can mean:

• you singular, in an informal/familiar way
• you plural

In this sentence, थकी हो does not tell you by itself whether तुम is one female person or more than one female person, because the feminine form थकी looks the same in both singular and plural. Context tells you which one is meant.

The adjective would change to match gender.

Examples:

• female you, female I: न तो तुम थकी हो, न ही मैं थकी हूँ।
• male you, female I: न तो तुम थके हो, न ही मैं थकी हूँ।
• female you, male I: न तो तुम थकी हो, न ही मैं थका हूँ।
• male you, male I: न तो तुम थके हो, न ही मैं थका हूँ।

A useful thing to notice:

• with मैं, masculine singular is थका हूँ
• with तुम, masculine is usually थके हो

That is a question of register and politeness.

• तुम is informal or familiar
• आप is polite or formal

So if you wanted to say the same thing politely to one woman, you could say:

• न तो आप थकी हैं, न ही मैं थकी हूँ।

Notice that आप takes हैं, not हो.

No. It is natural, but not the only option.

Other common versions are:

• न तुम थकी हो, न मैं थकी हूँ।
  A simpler neither ... nor ... form.

• तुम थकी नहीं हो, और मैं भी थकी नहीं हूँ।
  More like You are not tired, and I am not tired either.

So न तो ... न ही ... is a good, clear, slightly more emphatic version, but Hindi has other natural ways to express the same idea.