قالت الموظفة إن هذا الحساب يحتاج إلى بطاقة جديدة.

Because the subject is الموظفة, which is feminine singular: the female employee.

In the past tense:

• قال = he said
• قالت = she said

So قالت الموظفة means the female employee said.

That word order is very normal in Arabic. A verb-first sentence is common in MSA:

• قالت الموظفة = the employee said

You can also say:

• الموظفة قالت

but that usually gives a bit more emphasis to the employee. The version with the verb first is the more neutral, straightforward order here.

Yes. الموظفة is specifically feminine, so it means female employee, female clerk, or female staff member, depending on context.

Related forms:

• موظف = male employee
• موظفة = female employee

The الـ at the beginning makes it definite, so الموظفة = the female employee.

إنَّ is the particle that introduces a clause meaning that in formal Arabic.

So:

• قالت الموظفة إن هذا الحساب...
  = The employee said that this account...

In normal unvowelled writing, you often see it as إن, but in fully vowelled Arabic it is usually إنَّ, pronounced inna.

After verbs of saying, Arabic normally uses إنَّ to introduce the reported statement.

So:

• قال إن... = he said that...
• قالت إن... = she said that...

أنَّ is more common after verbs like:

• عرف = knew
• ظن = thought
• سمع in some structures
• أدرك = realized

So in this sentence, إنَّ is the expected choice.

Because الحساب is grammatically masculine singular.

The demonstratives are:

• هذا = this, for masculine singular
• هذه = this, for feminine singular

So:

• هذا الحساب = this account
• هذه البطاقة = this card

Even if an English noun has no gender, Arabic nouns do, and the demonstrative has to match.

In MSA, demonstratives like هذا usually come before the noun:

• هذا الحساب = this account
• هذه البطاقة = this card

That is the normal standard pattern.
In some spoken dialects, you may hear the demonstrative after the noun, but in MSA the usual form is هذا الحساب.

Because the subject of يحتاج is الحساب, and الحساب is masculine singular.

So the verb must also be masculine singular:

• يحتاج = it/he needs
• تحتاج = she/it needs

Here:

• الحساب يحتاج = the account needs

The account is grammatically masculine, so يحتاج is correct.

حساب can mean several things depending on context, including:

• account
• calculation
• bill/tab

In this sentence, it means account, because the context is something that needs a new card.

Also, حساب is grammatically masculine, which is why the sentence uses هذا and يحتاج.

The verb يحتاج often takes إلى before the thing needed.

So:

• يحتاج إلى بطاقة = it needs a card
• literally: it needs to a card

This is just the normal pattern of the verb in MSA:

• احتاج / يحتاج إلى ...

English says need something, but Arabic commonly says need to something with إلى.

Because the meaning is a new card, not the new card.

So Arabic uses an indefinite noun:

• بطاقة = a card
• البطاقة = the card

Since the sentence means the account needs some new card / a new card, the indefinite form is the natural one.

In Arabic, adjectives normally come after the noun they describe.

So:

• بطاقة جديدة = a new card

not the other way around.

This is one of the most important differences from English:

• English: new card
• Arabic: card new

Because it must agree with بطاقة, and بطاقة is feminine.

Arabic adjectives agree with the noun in:

• gender
• number
• definiteness
• case

So:

• بطاقة جديدة = a new card
• البطاقة الجديدة = the new card

Both the noun and the adjective are feminine here, which is why the adjective ends in ـة as well.

Yes. In normal Arabic writing, short vowels are usually not written, but in a fully vowelled version you would see the grammar more clearly.

A possible fully vowelled form is:

قالتِ الموظفةُ إنَّ هذا الحسابَ يحتاجُ إلى بطاقةٍ جديدةٍ

Some important points:

• الموظفةُ is nominative as the subject of قالت
• إنَّ makes its noun phrase accusative, so you get الحسابَ in a fully vowelled form
• after إلى, the noun is genitive: بطاقةٍ
• the adjective matches it: جديدةٍ

Also, هذا itself does not visibly change form here.

Yes. That is grammatical.

The difference is mostly emphasis and style:

• قالت الموظفة... = neutral, very natural narrative/reporting style
• الموظفة قالت... = puts more focus on the employee

So both are possible, but the original version sounds especially natural in formal written Arabic.