في المتحف الوطني معرض مؤقت بالإضافة إلى مجموعة أثرية.

This is a very common Arabic pattern. In the present tense, Arabic often uses a nominal sentence with no written word for is / are.

So:

• في المتحف الوطني = in the national museum
• معرض مؤقت = a temporary exhibition

Together, the sentence naturally means:

• In the national museum, there is a temporary exhibition...

Arabic often expresses existence this way instead of using a separate word like there is.

Arabic often puts the place expression first when introducing something that exists somewhere.

So the structure is roughly:

• في المتحف الوطني = location
• معرض مؤقت = the thing that exists there

This is very natural in Arabic and is similar to saying:

• At the national museum, there is a temporary exhibition...

Grammatically, في المتحف الوطني is a prepositional phrase placed first, and معرض comes after it as the main noun being introduced.

Because the sentence is introducing an exhibition, not referring to a specific already-known one.

• معرض مؤقت = a temporary exhibition
• المعرض المؤقت = the temporary exhibition

In Arabic, this kind of existence sentence commonly uses an indefinite noun after the place phrase:

• في البيت رجل = There is a man in the house
• في المتحف معرض = There is an exhibition in the museum

If you said في المتحف الوطني المعرض المؤقت, it would sound more like the temporary exhibition is in the national museum, referring to a known exhibition.

No. Here, الوطني is an adjective, not the second noun of an iḍāfa.

So:

• المتحف = the museum
• الوطني = national

Together:

• المتحف الوطني = the national museum

You can tell it is an adjective because الوطني matches المتحف in definiteness:

• المتحف = definite
• الوطني = also definite

In an iḍāfa, the second word usually would not take ال in this way if it were just a normal noun phrase of possession.

In Arabic, adjectives usually come after the noun and agree with it.

So:

• معرض مؤقت
  • معرض = exhibition
  • مؤقت = temporary

And:

• مجموعة أثرية
  • مجموعة = collection
  • أثرية = archaeological / heritage-related

The adjective must agree with the noun in things like gender and definiteness.

That is why:

• مؤقت is masculine singular, matching معرض
• أثرية is feminine singular, matching مجموعة

Because it describes مجموعة, and مجموعة is a feminine noun.

So:

• مجموعة = feminine singular
• therefore the adjective must be feminine singular too
• أثرية = feminine form of the adjective

If the noun were masculine, the adjective would normally be masculine as well.

بالإضافة إلى is a fixed expression meaning:

• in addition to
• besides
• along with

So here:

• بالإضافة إلى مجموعة أثرية = in addition to an archaeological collection

It adds another item to what is being mentioned. The sentence is saying that the museum has:

• a temporary exhibition
• plus an archaeological collection

This expression is slightly more formal than a simple و (and).

Because إلى is a preposition, and nouns after Arabic prepositions are normally in the genitive case.

So in full case endings, you would have:

• إلى مجموعةٍ أثريةٍ

Both مجموعةٍ and its adjective أثريةٍ take the genitive ending.

Even though everyday Arabic writing usually leaves out the short vowels, the underlying grammar is still there.

With full vowel endings, the sentence would be:

في المتحفِ الوطنيِّ معرضٌ مؤقَّتٌ بالإضافةِ إلى مجموعةٍ أثريَّةٍ.

Here is why:

• في = preposition
• المتحفِ = genitive after في
• الوطنيِّ = adjective matching المتحفِ, so also genitive
• معرضٌ = nominative
• مؤقَّتٌ = adjective matching معرضٌ, so nominative
• بالإضافةِ = genitive because of the preposition بـ
• إلى = preposition
• مجموعةٍ = genitive after إلى
• أثريَّةٍ = adjective matching مجموعةٍ, so genitive

Yes. That would also be correct.

• يوجد في المتحف الوطني معرض مؤقت...
• = There exists / there is a temporary exhibition in the national museum...

But Arabic very often prefers the simpler structure without يوجد, especially in neutral descriptive writing.

So both are possible, but:

• في المتحف الوطني معرض مؤقت... sounds natural and elegant
• يوجد في المتحف الوطني... is a bit more explicit

Using و would simply mean and:

• في المتحف الوطني معرض مؤقت ومجموعة أثرية

That is correct, but بالإضافة إلى gives a slightly different nuance:

• it emphasizes that the second item is an added extra
• it sounds a bit more formal or informational

So:

• و = simple coordination
• بالإضافة إلى = in addition to / besides

Both are possible, but they are not exactly identical in tone.