هذا المتحف الوطني.

Because Arabic often uses a nominal sentence in the present tense, with no explicit verb for is/am/are.

So:

• هذا المتحف الوطني = This is the national museum

In the present tense, Arabic usually just puts the parts of the sentence next to each other.
If you wanted the past or future, then a verb would appear.

For example:

• كان هذا المتحف الوطني = This was the national museum

هذا is the masculine singular demonstrative, meaning this.

It is used because المتحف (museum) is grammatically masculine singular.

So Arabic matches the demonstrative to the noun:

• هذا المتحف = this museum
• هذه المدرسة = this school (because school is feminine)

Because المتحف is a masculine noun.

In Arabic, demonstratives agree with the noun’s grammatical gender:

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

Since museum is masculine, هذا is the correct choice.

That is the normal order in Arabic when you say this/that + noun.

So Arabic says:

• هذا المتحف = literally this the-museum

This is different from English word order only in appearance, because the Arabic noun is usually definite when used with a demonstrative.

Because الوطني is an adjective describing المتحف, and Arabic adjectives must match the noun in definiteness.

Here:

• المتحف = the museum
• الوطني = the national

So together:

• المتحف الوطني = the national museum

If the noun is definite, the adjective must also be definite.

Compare:

• متحف وطني = a national museum
• المتحف الوطني = the national museum

Yes. الوطني is an adjective meaning national.

It comes after the noun it describes, which is the normal position for adjectives in Arabic.

So:

• المتحف الوطني = literally the museum the-national

In natural English, that becomes the national museum.

Arabic adjectives agree with the noun in several ways, including:

• gender
• number
• definiteness
• case (in fully vocalized formal Arabic)

Here, both words are:

• masculine
• singular
• definite

So the match is correct:

• المتحف — masculine singular definite
• الوطني — masculine singular definite

If the noun were feminine, the adjective would also change. For example:

• المدرسة الوطنية = the national school

A fully vocalized version would normally be:

• هٰذَا الْمَتْحَفُ الْوَطَنِيُّ

A careful pronunciation is roughly:

• hādhā al-matḥafu al-waṭaniyyu

A few notes:

• ح in متحف is a deeper h sound than English h
• ط in وطني is an emphatic t
• the ending -يّ in وطنيّ sounds like -iyy

In everyday reading and speech, learners often ignore the final case vowels at first, and that is very common.

In fully formal Arabic, the words would have nominative endings here:

• الْمَتْحَفُ
• الْوَطَنِيُّ

That is because the sentence is in the nominative structure used for this kind of nominal sentence.

However, in normal printed Arabic:

• short vowels are usually not written
• many speakers pause at the end and do not pronounce the full final ending clearly

So as a learner, it is good to know the formal endings, but you do not need to panic if you do not hear or say them perfectly at first.

It can function as a complete sentence when said on its own:

• هذا المتحف الوطني = This is the national museum

But inside a larger sentence, the same sequence can also behave like a noun phrase:

• زرت هذا المتحف الوطني = I visited this national museum

So context tells you whether it is being used as:

• a standalone sentence, or
• a phrase inside a bigger sentence

You would usually make the noun and adjective indefinite:

• هذا متحف وطني

That means:

• this is a national museum

Compare the two:

• هذا المتحف الوطني = This is the national museum
• هذا متحف وطني = This is a national museum

So the presence or absence of الـ changes the meaning from definite to indefinite.

Yes. In both words, the ل of الـ is pronounced normally, because م and و are moon letters, not sun letters.

So you say:

• al-matḥaf
• al-waṭanī

You do not assimilate the l sound here.

For comparison, with a sun letter you would get assimilation, such as:

• الشمس pronounced ash-shams

But in your sentence, the l stays audible.