النظام الداخلي على الحاسوب.

Usually no. By itself, it is most naturally understood as a noun phrase, not a full sentence.

It works well as:

• a title
• a heading
• a label
• a short menu/item name

Arabic often allows short verbless phrases in places where English might also use a fragment, such as headings or interface text.

Because in Arabic, an adjective normally comes after the noun it describes.

So:

• النظام = the system
• الداخلي = internal

Together:

• النظام الداخلي = the internal system

This is the normal Arabic order:

• noun + adjective

not:

• adjective + noun

Because الداخلي is an adjective, and Arabic adjectives must agree with the noun they describe in several ways, including definiteness.

So if the noun is definite, the adjective must also be definite:

• نظام داخلي = an internal system
• النظام الداخلي = the internal system

This agreement also applies to:

• gender
• number
• case

In this phrase, both words are masculine singular definite.

No. It is not an iḍāfa. It is a noun + adjective combination.

Why not?

Because in an iḍāfa, the second noun is not an adjective, and the structure works differently. For example:

• نظام الحاسوب = the computer's system / the system of the computer

Here, الحاسوب is a noun, not an adjective.

But in:

• النظام الداخلي

الداخلي is an adjective meaning internal, and it agrees with النظام.

A useful comparison:

• النظام الداخلي = the internal system
• نظام الحاسوب = the computer system / the system of the computer
• النظام الداخلي للحاسوب = the internal system of the computer

Yes, this is a very natural question.

على often means on in the sense of something being:

• shown on a device
• done on a device
• available on a device

So على الحاسوب can mean something like on the computer.

By contrast, في الحاسوب would more strongly suggest in the computer or inside the computer.

So the difference is often about usage nuance:

• على الحاسوب = on the computer
• في الحاسوب = in the computer / inside the computer

In real usage, the best choice depends on context.

A common pause-style pronunciation is:

an-niẓām ad-dākhilī ʿalā l-ḥāsūb

Two important pronunciation points are happening here:

1. النظام
   The ل of الـ is not pronounced normally before ن, because ن is a sun letter.
   So ال + نظام is pronounced an-niẓām, not al-niẓām.

2. الداخلي
   The same thing happens because د is also a sun letter.
   So it is pronounced ad-dākhilī, not al-dākhilī.

3. الحاسوب
   Here, ح is a moon letter, so the ل is pronounced.
   That is why you hear al-ḥāsūb in isolation, or l-ḥāsūb after على in connected speech.

If you read it with full case endings in a nominative, heading-like form, it could be:

an-niẓāmu d-dākhiliyyu ʿalā l-ḥāsūbi

Why those endings?

• النظامُ is nominative
• الداخليُّ matches it and is also nominative
• الحاسوبِ is genitive because it comes after the preposition على

In normal modern writing, these short final vowels are usually not written, and in everyday speech they are often not pronounced either.

Usually no.

The usual MSA term for operating system is:

نظام التشغيل

By contrast, النظام الداخلي is more literally the internal system.

Also, depending on context, النظام الداخلي can have other meanings, such as internal regulations or bylaws. So context matters a lot.

In this phrase, على الحاسوب gives it a computer-related setting, but it still does not automatically mean operating system.