क्या आपको अस्पताल का रास्ता पता है?

At the beginning of a sentence, क्या is a yes/no question marker. It signals that the speaker is asking a question like do/does/is/are in English.

So:

• क्या आपको अस्पताल का रास्ता पता है? = Do you know the way to the hospital?

In casual speech, Hindi can sometimes ask the same question without initial क्या, just using intonation:

• आपको अस्पताल का रास्ता पता है?

That is still natural.

Because Hindi uses the pattern someone + को + पता है for someone knows / someone is aware of something.

So:

• आपको पता है = literally something like to you it is known

This is a very common Hindi structure. English uses you know, but Hindi often uses आपको ... पता है.

Using just आप here would sound wrong in standard Hindi:

• correct: आपको अस्पताल का रास्ता पता है?
• not natural here: आप अस्पताल का रास्ता पता है?

Because पता होना is the most natural way to say to know information, a fact, a route, an address, an answer, etc.

So रास्ता पता है means know the way / know the route.

You can say:

• क्या आप अस्पताल का रास्ता जानते हैं?

and people will understand it, but क्या आपको अस्पताल का रास्ता पता है? sounds more idiomatic in everyday Hindi.

A rough guide:

• पता होना = know a fact / know information / know the way
• जानना = know in a broader sense, including being acquainted with someone, knowing a language, knowing something in general

Yes. पता can mean address, but in the expression पता होना, it means to be known / to be aware / to know.

Examples:

• मुझे आपका पता नहीं है। = I don’t know your address.
• मुझे नहीं पता। = I don’t know.
• उसे रास्ता पता है। = He/She knows the way.

So in your sentence, पता is part of the fixed expression पता होना.

Literally, it means the hospital’s way/path. But in natural English, it means the way to the hospital.

Hindi often uses this pattern:

• X का रास्ता = the way to X

So:

• स्टेशन का रास्ता = the way to the station
• बाजार का रास्ता = the way to the market
• अस्पताल का रास्ता = the way to the hospital

Sometimes Hindi can also say अस्पताल तक का रास्ता, which is a bit more explicit: the way up to the hospital.

Because का / के / की agrees with the noun that follows it, and here that noun is रास्ता, which is masculine singular.

So:

• अस्पताल का रास्ता — because रास्ता is masculine singular

If the following noun were different, the form would change:

• अस्पताल की सड़क = the road to the hospital
  because सड़क is feminine
• अस्पताल के रास्ते = the ways/routes to the hospital
  because रास्ते is plural

It does not depend on अस्पताल here.

That is a great question. In this sentence, आप is not the word controlling the verb form, because it appears as आपको in a dative-style construction.

The structure is:

• आपको = to you
• अस्पताल का रास्ता = the way to the hospital
• पता है = is known

So the sentence is built more like Is the way to the hospital known to you?

That is why है is fine here. The verb is not behaving like it would in a normal आप + verb sentence such as:

• आप जानते हैं = you know
• आप जाते हैं = you go

The given word order is natural and standard:

• क्या आपको अस्पताल का रास्ता पता है?

But Hindi word order is somewhat flexible. You may also hear:

• आपको अस्पताल का रास्ता पता है?
• अस्पताल का रास्ता आपको पता है?
• आपको अस्पताल का रास्ता पता है क्या? (more colloquial in some speech styles)

The version with क्या at the beginning is the clearest standard yes/no question form for learners.

It is polite/formal because it uses आप.

Here are the main levels:

• आपको अस्पताल का रास्ता पता है? = polite/formal
• तुम्हें अस्पताल का रास्ता पता है? = informal/friendly
• तुझे अस्पताल का रास्ता पता है? = very informal/intimate

So if you are asking a stranger, आपको is the safest choice.

Not very well. A word-for-word translation would sound something like:

• What, to you, the hospital’s way known is?

That sounds unnatural in English, but it helps show the grammar.

A more useful breakdown is:

• क्या = question marker
• आपको = to you
• अस्पताल का रास्ता = the way to the hospital
• पता = known / knowledge
• है = is

So the natural English meaning is simply:

• Do you know the way to the hospital?

Yes, it is natural and correct.

However, if you are directly asking someone for directions, Hindi speakers may also use slightly different sentences, such as:

• अस्पताल कैसे जाना है? = How do I get to the hospital?
• अस्पताल का रास्ता कहाँ है? = Where is the way to the hospital?
• क्या आप मुझे अस्पताल का रास्ता बता सकते हैं? = Can you tell me the way to the hospital?

Your original sentence is especially natural if you are first checking whether the other person knows the way.