صلاحية جواز السفر وتاريخ الانتهاء مهمان اليوم.

Because this is a present-tense nominal sentence in Arabic. In Modern Standard Arabic, the verb to be is usually not expressed in the present tense.

So:

• صلاحية جواز السفر وتاريخ الانتهاء مهمان اليوم
  literally works like: Passport validity and the expiration date important today

But in natural English, we translate it with are.

If you wanted the past or future, Arabic would normally use an actual verb, for example:

• كانا مهمَّيْنِ = they were important
• سيكونان مهمَّيْنِ = they will be important

It is a nominal sentence made of:

• صلاحية جواز السفر وتاريخ الانتهاء = the subject/topic
• مهمان = the predicate, describing those two things
• اليوم = a time expression, today

So the pattern is basically:

• [subject] + [predicate] + [time expression]

More specifically:

• صلاحية جواز السفر = the validity of the passport
• وتاريخ الانتهاء = and the expiration date
• مهمان = are important for two things
• اليوم = today

Because the sentence is talking about exactly two things:

• صلاحية جواز السفر
• تاريخ الانتهاء

In Arabic, when something refers to exactly two items, the language often uses the dual.

So:

• مهم = important, masculine singular
• مهمان = important, masculine dual

Fully vocalized, it is مُهِمّانِ.

This is the normal way to say that two things are important.

Because the two nouns are mixed in gender:

• صلاحية is feminine
• تاريخ is masculine

When Arabic has a mixed group like this, the agreement usually defaults to the masculine form.

So the predicate becomes:

• مهمان = masculine dual

If both items were feminine, you would expect:

• مهمتان = feminine dual

Because مهمان here is not an attributive adjective inside the noun phrase. It is the predicate of the whole sentence.

That distinction is very important:

• attributive adjective: directly describes a noun and must match it in definiteness
• predicate adjective: comes as the statement about the subject and is usually indefinite

Here, مهمان means are important, not the two important ones.

Compare:

• الجواز المهم = the important passport
  Here المهم is an adjective directly modifying الجواز, so it is definite.

But in your sentence:

• صلاحية جواز السفر وتاريخ الانتهاء مهمان
  Here مهمان is the predicate, so it stays indefinite.

Yes. صلاحية جواز السفر is an iḍāfa construction, meaning a noun relationship like the validity of the passport.

In an iḍāfa:

• the first noun usually does not take الـ
• the whole phrase can still be definite depending on the second noun

So here:

• صلاحية = validity
• جواز السفر = passport

Together:

• صلاحية جواز السفر = the passport’s validity / the validity of the passport

Also, جواز السفر is itself another iḍāfa:

• جواز = pass
• السفر = travel

So literally it is something like travel pass, which is the normal Arabic way to say passport.

Yes.

• تاريخ = date
• الانتهاء = expiration / ending

So:

• تاريخ الانتهاء = the date of expiration = the expiration date

Again, the first noun in the iḍāfa, تاريخ, does not take الـ, while the second noun الانتهاء is definite.

This is a very common Arabic pattern for noun combinations that English often expresses with of.

اليوم is functioning as an adverbial time expression. In Arabic, words like today, tomorrow, and similar time expressions often appear without a preposition.

So:

• اليوم = today

You do not need في here.

As for position, putting اليوم at the end is very natural. Arabic often places time expressions after the main statement:

• صلاحية جواز السفر وتاريخ الانتهاء مهمان اليوم

But other word orders are also possible for emphasis, such as putting اليوم earlier.

When fully vocalized, اليوم here is usually اليومَ, because it is functioning as a time adverb.

With full case endings, it would be:

صلاحيّةُ جوازِ السفرِ وتاريخُ الانتهاءِ مُهِمّانِ اليومَ

Here is why:

• صلاحيّةُ: nominative, because it is part of the subject
• جوازِ: genitive, because it is the second term of the outer iḍāfa
• السفرِ: genitive, because it is the second term of the inner iḍāfa
• تاريخُ: nominative, coordinated with صلاحيّةُ
• الانتهاءِ: genitive, because of iḍāfa
• مُهِمّانِ: nominative dual, because it is the predicate
• اليومَ: accusative as an adverbial expression of time

In normal everyday Arabic writing, these short vowel endings are usually omitted, but the grammar is still there underneath.

For exactly two things, the dual is the standard and most precise choice in formal Arabic, so مهمان is the expected form.

Arabic distinguishes clearly between:

• singular = one
• dual = two
• plural = three or more

So since the sentence mentions exactly two items, the dual is the natural form.

That is one of the features English speakers often need time to get used to, because English does not have a separate dual form.