هذه بطاقة موظف.

In Arabic, the verb to be is usually not stated in the present tense.

So:

• هذه بطاقة موظف = This is an employee card
• literally: This employee-card

This is called a nominal sentence. Arabic often just puts the two parts side by side when talking about the present.

If you wanted past tense, then Arabic would use a verb, for example:

• كانت هذه بطاقة موظف = This was an employee card

Because بطاقة is a feminine singular noun, and the demonstrative must agree with it.

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

Since بطاقة is feminine, you say:

• هذه بطاقة...

not

• هذا بطاقة...

A big clue is the ending ة (called taa marbuuTa).

Many Arabic nouns ending in ة are feminine, and بطاقة is one of them.

So:

• بطاقة = card, بطاقة /biTāqah/
• because it is feminine, it takes feminine agreement:
  • هذه بطاقة
  • not هذا بطاقة

Keep in mind that ة often signals feminine gender, though not absolutely every word behaves the same way in all situations.

No. موظف here is a noun, not an adjective.

• موظف = employee
• بطاقة موظف literally means card of an employee

This is an iḍāfa construction, often called the construct phrase:

• بطاقة = card
• موظف = employee
• بطاقة موظف = employee card / an employee’s card

In English, we often translate this naturally as employee card, even though Arabic is structurally closer to card of an employee.

Because the phrase is indefinite here.

• بطاقة موظف = an employee card / a card of an employee
• بطاقة الموظف = the employee’s card

So the sentence as written is talking about a card, not the card.

Also, in an iḍāfa construction:

• the first noun usually does not take ال
• the second noun controls whether the whole phrase is definite or indefinite

Compare:

• بطاقة موظف = an employee card
• بطاقة الموظف = the employee’s card

With full case endings, it is:

• هذهِ بِطاقةُ مُوَظَّفٍ

Here is why:

• هذهِ = demonstrative
• بطاقةُ = predicate of the sentence, so it is nominative
• موظفٍ = second term of an iḍāfa, so it is genitive

A useful thing to notice:

• If بطاقة were by itself and indefinite, it could be بطاقةٌ
• but in iḍāfa, the first noun loses tanwīn
• so it becomes بطاقةُ موظفٍ, not بطاقةٌ موظفٍ

A careful pronunciation with case endings is roughly:

• hādhihi biṭāqatu muwaẓẓafin

In pause, many speakers would say something closer to:

• hādhihi biṭāqat muwaẓẓaf

A few pronunciation notes:

• هذه = hādhihi
• بطاقة = biṭāqah
• موظف = muwaẓẓaf
• the ظّ in موظف is doubled, so the consonant is held slightly longer
• ṭ and ẓ are emphatic consonants

Because it is the first noun in an iḍāfa construction.

Normally, an indefinite noun can take tanwīn:

• بطاقةٌ = a card

But in iḍāfa, the first noun:

• does not take tanwīn
• does not usually take ال

So:

• بطاقةُ موظفٍ = an employee card

not

• بطاقةٌ موظفٍ

This is one of the most important signs that you are looking at an iḍāfa phrase.

Yes. Literally, بطاقة موظف means card of an employee, so that can be understood as:

• an employee card
• an employee’s card

Context decides the most natural English translation.

In many real-life situations, this phrase would often refer to something like:

• an employee ID card
• an employee badge

So the exact English wording may vary even though the Arabic structure stays the same.

You would usually say:

• هذه بطاقة الموظف

That changes the second noun from indefinite to definite:

• موظف = an employee
• الموظف = the employee

So:

• هذه بطاقة موظف = This is an employee card / an employee’s card
• هذه بطاقة الموظف = This is the employee’s card

That one small change makes the whole iḍāfa phrase definite.