मैं यहाँ हस्ताक्षर करूँगी; डाकघर पार्सल कितने दिन में पहुँचाएगा?

Because the speaker is female. In the future tense, करूँगी is the feminine singular form of I will do, while करूँगा is the masculine singular form.

• मैं यहाँ हस्ताक्षर करूँगी = said by a woman
• मैं यहाँ हस्ताक्षर करूँगा = said by a man

So the verb agrees with the speaker’s gender here.

It is a noun + करना construction.

• हस्ताक्षर = signature / signing
• हस्ताक्षर करना = to sign

So हस्ताक्षर करूँगी literally means something like I will do a signature, but in natural English it is simply I will sign.

This is a very common Hindi pattern:

• फ़ैसला करना = to make a decision
• फ़ोन करना = to phone
• कोशिश करना = to try

Yes, हस्ताक्षर is fairly formal and standard. It is especially common in offices, forms, banks, and official situations.

In everyday speech, many people also say:

• साइन करना = to sign

So:

• मैं यहाँ हस्ताक्षर करूँगी sounds more formal
• मैं यहाँ साइन करूँगी sounds more colloquial and modern

Both are understandable.

Yes, it could be omitted if the subject is already clear.

Hindi often leaves out subject pronouns when the verb already shows who is being talked about. So both are possible:

• मैं यहाँ हस्ताक्षर करूँगी
• यहाँ हस्ताक्षर करूँगी

The first is a bit clearer or more explicit. The second is natural if the context already makes it obvious that the speaker means I.

यहाँ means here.

In this context, it means here, at this place / on this spot. If someone is looking at a form or a document, मैं यहाँ हस्ताक्षर करूँगी means I’ll sign here.

So यहाँ is pointing to the place where the signing will happen.

It is the future form of करना for first person singular feminine.

Very roughly:

• verb root: कर-
• future/subjunctive-style stem: करूँ-
• feminine ending: -गी

So:

• करूँगा = I will do (masculine speaker)
• करूँगी = I will do (feminine speaker)

This same pattern appears with many verbs:

• जाऊँगी = I will go
• लिखूँगी = I will write
• देखूँगी = I will see

Because पहुँचाएगा comes from पहुँचाना, which means to deliver / to cause something to reach.

Compare:

• पहुँचना = to arrive, to reach
  
  • पार्सल पहुँच जाएगा = The parcel will arrive
• पहुँचाना = to deliver, to make something reach
  
  • डाकघर पार्सल पहुँचाएगा = The post office will deliver the parcel

So the sentence uses the causative/transitive verb because the post office is acting on the parcel.

डाकघर means post office.

It is made from:

• डाक = post / mail
• घर = house / building

So literally it is something like mail-house, but the normal meaning is simply post office.

Because this sentence is in the future, and Hindi normally does not use ने with this kind of future clause.

• डाकघर पार्सल पहुँचाएगा = The post office will deliver the parcel

The marker ने is most commonly used with perfective transitive verbs, such as:

• डाकघर ने पार्सल पहुँचाया = The post office delivered the parcel

So in the future sentence, डाकघर stays unmarked.

Because Hindi often leaves direct objects unmarked, especially when they are inanimate things like a parcel.

So:

• डाकघर पार्सल पहुँचाएगा is perfectly normal

Using को is possible in some contexts, especially for emphasis or definiteness, but it is not required here.

This is very common in Hindi:

• मैं किताब पढ़ूँगा = I will read a book / the book
• वह चाय पिएगी = She will drink tea

It means in how many days.

In natural English, depending on context, it can mean:

• How many days will it take?
• Within how many days?
• In how many days will it be delivered?

So डाकघर पार्सल कितने दिन में पहुँचाएगा? is asking about the delivery time.

Both can be heard.

Strictly speaking, after में, many learners expect an oblique plural like दिनों, and कितने दिनों में is certainly correct.

But कितने दिन में is also extremely common in everyday Hindi, especially in time expressions. It sounds natural and idiomatic.

So:

• कितने दिन में? = very common
• कितने दिनों में? = also correct

Yes. The semicolon is just linking two related statements:

• मैं यहाँ हस्ताक्षर करूँगी। डाकघर पार्सल कितने दिन में पहुँचाएगा?

That would also be perfectly fine. In speech, there would simply be a pause between the two parts. The semicolon is a punctuation choice, not a grammar requirement.