تاريخ الانتهاء ومدة المعالجة واضحان في الاستمارة.

Because this is a present-tense nominal sentence in Arabic. In Modern Standard Arabic, you usually do not say a separate word for is / are in the present.

So:

تاريخ الانتهاء ومدة المعالجة واضحان
literally works like
The expiration date and the processing time clear

In natural English, we add are, but Arabic does not need it here.

If you wanted the past, you would use a verb such as كان:

كان تاريخ الانتهاء ومدة المعالجة واضحَيْنِ
The expiration date and the processing time were clear

Yes. تاريخ can mean both history and date, and the context tells you which one is meant.

In this sentence, تاريخ الانتهاء clearly means expiration date or date of expiry, not history of ending.

This is very common in Arabic:

• تاريخ الميلاد = date of birth
• تاريخ اليوم = today’s date
• تاريخ العرب = the history of the Arabs

Because both تاريخ الانتهاء and مدة المعالجة are iḍāfa constructions, often called a construct phrase.

In an iḍāfa:

• the first noun does not take الـ
• the whole phrase can still be definite if the second noun is definite

So:

• تاريخ الانتهاء = the expiration date
• مدة المعالجة = the processing time / duration of processing

You should not say:

• التاريخ الانتهاء
• المدة المعالجة

Those would be wrong for this structure.

They are definite.

Even though تاريخ and مدة themselves do not have الـ, the whole iḍāfa becomes definite because the second word is definite:

• الانتهاء
• المعالجة

So:

• تاريخ الانتهاء = the expiration date
• مدة المعالجة = the processing time

This is a key rule of iḍāfa in Arabic: the definiteness of the whole phrase depends on the second noun.

Because مدة ends in ة (tāʾ marbūṭa), and in connected speech that ة is pronounced as t when another word follows in grammar.

So by itself, in pause, you often hear:

• مدة = mudda

But in iḍāfa, it is pronounced:

• مدة المعالجة = muddat al-muʿālaja

This is very normal:

• سيارة alone may sound like sayyāra
• but سيارة المدير is sayyārat al-mudīr

Because the sentence has two things as its subject:

• تاريخ الانتهاء
• مدة المعالجة

Since there are exactly two items, the predicate is put in the dual:

• واضحان = clear for two

This is one of the places where Arabic dual grammar is very visible.

Compare:

• تاريخ الانتهاء واضح = the expiration date is clear
• تاريخ الانتهاء ومدة المعالجة واضحان = the expiration date and the processing time are clear
• التواريخ واضحة = the dates are clear

Because the subject is a pair with mixed gender:

• تاريخ is masculine
• مدة is feminine

When Arabic has a mixed group, masculine agreement is normally used as the default. So the dual predicate is masculine dual:

واضحان

If both nouns were feminine, then you would use واضحتان.

Because here واضحان is not an attributive adjective inside a noun phrase. It is the predicate of the sentence, called خبر in Arabic grammar.

Predicates in sentences like this are usually indefinite, even when the subject is definite.

So:

• تاريخ الانتهاء ومدة المعالجة واضحان = the expiration date and the processing time are clear

But if واضحان were directly modifying a definite noun phrase, then it would normally also be definite:

• الأمران الواضحان = the two clear matters

So the lack of الـ is correct and expected here.

Here واضحان is in the nominative dual form.

The dual endings are:

• ـانِ for nominative
• ـيْنِ for accusative and genitive

In this sentence, واضحان is nominative because it is the predicate of a basic nominal sentence.

It would become واضحَيْنِ in a context where the grammar requires the accusative, for example after كان:

كان تاريخُ الانتهاءِ ومدّةُ المعالجةِ واضحَيْنِ
The expiration date and the processing time were clear

It is best understood here as a predicate adjective, not as an adjective directly attached to a noun.

In Arabic grammar, it is the خبر of the sentence.

That means:

• تاريخ الانتهاء ومدة المعالجة = the subject
• واضحان = the predicate
• في الاستمارة = a prepositional phrase giving extra information

A useful comparison:

• التاريخ الواضح = the clear date
  Here الواضح is a normal adjective modifying التاريخ

• التاريخ واضح = the date is clear
  Here واضح is the predicate

Your sentence uses the second pattern.

Because Arabic often uses في where English might say in or on, depending on context.

Literally, في الاستمارة is in the form, but in natural English, information written on a document is often said to be on the form.

So both ideas are connected, but the best English translation is often:

• on the form
• or in the form, depending on context and style

This is a normal difference between the two languages, not a special rule just for this sentence.

A fully vowelled version is:

تاريخُ الانتهاءِ ومدّةُ المعالجةِ واضحانِ في الاستمارةِ

This shows the grammatical endings more clearly:

• تاريخُ = nominative
• الانتهاءِ = genitive, because of iḍāfa
• مدّةُ = nominative
• المعالجةِ = genitive, because of iḍāfa
• واضحانِ = nominative dual
• الاستمارةِ = genitive after في

In normal unvocalled writing, most of these short vowels are not written, but the dual ending in واضحان is still visible.

Yes, Arabic word order is somewhat flexible, but the original order is the most neutral and straightforward.

The given sentence:

تاريخ الانتهاء ومدة المعالجة واضحان في الاستمارة

is a very natural way to say it.

You could also move في الاستمارة earlier for emphasis:

في الاستمارة، تاريخ الانتهاء ومدة المعالجة واضحان

That can sound like: On the form, the expiration date and the processing time are clear

So the meaning stays basically the same, but the emphasis changes a little.