הפקידה בעירייה אמרה שבלי חותמת אי אפשר לסיים את הבקשה של התושבת החדשה.

Yes. הפקידה is the feminine form of פקיד (clerk / official).

• פקיד = a male clerk / official
• פקידה = a female clerk / official
• הפקידה = the female clerk

In this sentence, the verb אמרה also shows that the subject is feminine, so the clerk is clearly female.

בעירייה means in the municipality / at city hall.

It is made of:

• ב־ = in / at
• העירייה = the municipality / city hall

When ב־ is attached to a noun with ה־, they combine:

• ב + העירייה → בעירייה

This is very common in Hebrew:

• בבית = in the house
• במשרד = in the office
• בעירייה = in the municipality

Here ש means that.

So:

• אמרה ש... = said that...

In this sentence:

• אמרה שבלי חותמת...
• literally: she said that without a stamp...

Hebrew often attaches ש directly to the next word, so שבלי is just:

• ש = that
• בלי = without

Because Hebrew often uses an indefinite noun after בלי when English would say without a... or just without....

So:

• בלי חותמת = without a stamp / without a seal

Using בלי החותמת would mean without the stamp, referring to a specific known stamp.

So the sentence is talking about the general requirement for a stamp, not one particular stamp.

חותמת usually means stamp or official seal.

In bureaucratic contexts, it often refers to:

• a physical stamp
• an official seal impression
• sometimes a stamped approval

It does not normally mean signature.
A signature is חתימה.

So in this sentence, חותמת is most naturally a stamp / official seal.

אי אפשר is a very common Hebrew expression meaning:

• it’s impossible
• you can’t
• one cannot

Literally, it is something like there is no possibility.

It is impersonal, which means it does not refer to a specific subject like I, you, or they.
So:

• אי אפשר לסיים = it’s impossible to finish / you can’t finish

Hebrew uses this structure a lot:

• אי אפשר לדעת = it’s impossible to know / you can’t know
• אי אפשר להיכנס = you can’t enter
• אי אפשר לסיים = you can’t finish

Because אי אפשר is often followed by an infinitive.

• לסיים = to finish / to complete

So:

• אי אפשר לסיים = it’s impossible to finish

This is a standard pattern:

• אפשר לעשות = it’s possible to do
• אי אפשר לעשות = it’s impossible to do
• אפשר לראות = it’s possible to see
• אי אפשר לראות = it’s impossible to see

את marks a definite direct object.

Here, הבקשה is definite because it has ה־:

• בקשה = request / application
• הבקשה = the request / the application

So Hebrew uses את:

• לסיים את הבקשה = to finish the application

A quick comparison:

• ראיתי ספר = I saw a book
• ראיתי את הספר = I saw the book

So in your sentence, את is there because the application is a specific, definite object.

It can mean either, depending on context.

בקשה can be:

• request
• application
• sometimes even please in other contexts, though not here

Because this sentence is about the municipality and a stamp, application is often the most natural translation.
But request is not wrong grammatically.

So את הבקשה could be understood as:

• the application
• the request

Hebrew has two common ways to show possession:

1. של structure

   • הבקשה של התושבת החדשה = the application of the new resident

2. Construct chain (smikhut)

   • something like בקשת התושבת החדשה

Both are possible in many cases, but של often sounds more natural in everyday speech, especially when the noun phrase is longer or more complex.

So this sentence uses the very common spoken/written pattern:

• the application of the new resident
• הבקשה של התושבת החדשה

Yes. תושבת is feminine.

• תושב = male resident
• תושבת = female resident

So:

• התושבת = the female resident
• התושב = the male resident

Since the adjective החדשה is also feminine, the phrase clearly refers to a woman.

Because adjectives in Hebrew must agree with the noun in:

• gender
• number
• definiteness

The noun is:

• התושבת = feminine singular definite

So the adjective must also be:

• feminine singular definite → החדשה

Compare:

• תושב חדש = a new male resident
• תושבת חדשה = a new female resident
• התושב החדש = the new male resident
• התושבת החדשה = the new female resident

So the ה־ appears on the adjective too because the whole noun phrase is definite.

It describes התושבת, not הבקשה.

The phrase is:

• הבקשה של התושבת החדשה

This means:

• the application of the new female resident

If new described the application, the Hebrew would need a different structure, such as:

• הבקשה החדשה של התושבת = the new application of the resident

So in the original sentence, new belongs to resident.

Hebrew often starts with the subject, then gives more information about that subject, then the verb.

So:

• הפקידה בעירייה = the clerk at the municipality
• אמרה = said

This is a very natural Hebrew word order.

You can think of it as:

• [The clerk at city hall] [said] [that...]

Hebrew word order is somewhat flexible, but this version is neutral and natural.

Normally, no. עירייה means municipality / city hall / municipal authority, not just city.

• עיר = city
• עירייה = municipality / city hall

So הפקידה בעירייה means:

• the clerk at the municipality
• the clerk at city hall

not simply the clerk in the city.

You would change the feminine forms connected to the clerk:

• הפקיד בעירייה אמר שבלי חותמת אי אפשר לסיים את הבקשה של התושבת החדשה.

Changes:

• הפקידה → הפקיד
• אמרה → אמר

The rest stays the same, because the resident is still feminine in this version.

Not necessarily stronger, but it often sounds slightly more impersonal and matter-of-fact.

In this sentence:

• אי אפשר לסיים = you can’t finish / it’s impossible to finish

In bureaucratic Hebrew, this kind of impersonal wording is very common. It can sound like:

• this cannot be done
• it is not possible to complete this

So it fits the official tone of the sentence very well.

A helpful breakdown is:

• הפקידה בעירייה = the female clerk at the municipality
• אמרה = said
• ש = that
• בלי חותמת = without a stamp
• אי אפשר לסיים = it’s impossible to complete / you can’t complete
• את הבקשה = the application
• של התושבת החדשה = of the new female resident

So the sentence is basically:

• [The clerk at city hall] [said] [that] [without a stamp] [it is impossible to complete] [the application] [of the new resident].

That is a very typical Hebrew sentence pattern:
main clause first, then a ש־ clause giving what was said.