Learn Hardcore Malay: Di meja belajar, komputer saya mempunyai skrin besar, papan kekunci selesa, dan tetikus kecil. - On the study desk, my computer has a big screen, a comfortable keyboard, and a small mouse.

People often drop atas when the location is obvious (a computer is naturally on the desk, not under it), so di meja belajar is fine and common.
You usually add atas when you need to be very clear about “on top of” something, or to contrast with di bawah (under), di dalam (inside), etc.

So the sentence is natural as it is. Di meja belajar already suggests “on the desk” in this context.

What exactly does meja belajar mean? Is belajar acting like an adjective here?

Literally:

meja = table / desk
belajar = to study

In Malay, you often put one noun after another to show a specific type or function:

meja belajar = study desk (a desk for studying)
buku latihan = exercise book (book for practice)
kasut sukan = sports shoes (shoes for sports)

So belajar is still a verb in general, but in the phrase meja belajar it works like a modifier telling you the purpose of the desk. Malay doesn’t need a special adjective form like “study-desk”; it just uses verb or noun + noun.

Why is it komputer saya and not saya komputer or something like English “my computer”?

Malay shows possession mainly by putting the possessor after the thing:

komputer saya = my computer (literally “computer I”)
buku dia = his/her book
rumah kami = our house

You cannot say saya komputer to mean “my computer”; that sounds like “I am a computer”.

There is also a more colloquial pattern:

komputer saya = my computer (neutral, standard)
saya punya komputer = my computer (informal / spoken)

In a neutral written sentence like this, komputer saya is the most natural choice.

What is the difference between mempunyai and ada? Could I say komputer saya ada skrin besar instead?

Both can be used to express having, but they behave a bit differently.

mempunyai

More formal, often used in writing.
Must be followed by an object (something possessed).
Structure: subject + mempunyai + object(s)
- Komputer saya mempunyai skrin besar.

ada

Very common in spoken Malay.
Has two main uses:
1. Existence: “there is/are”
  - Di meja belajar, ada komputer. = There is a computer on the desk.
2. Possession, especially in speech:
  - Komputer saya ada skrin besar. = My computer has a big screen.

In your sentence, komputer saya mempunyai skrin besar, papan kekunci selesa, dan tetikus kecil is correct and sounds a bit more formal/neutral.
You can also say komputer saya ada skrin besar…, which sounds more casual / conversational. Both are acceptable.

Why does one verb mempunyai cover skrin besar, papan kekunci selesa, dan tetikus kecil all at once?

In Malay, one verb can take a list of objects, joined with commas and dan:

Komputer saya mempunyai skrin besar, papan kekunci selesa, dan tetikus kecil.
= My computer has (1) a big screen, (2) a comfortable keyboard, and (3) a small mouse.

Grammatically, this is:

komputer saya (subject)
mempunyai (verb)
skrin besar, papan kekunci selesa, dan tetikus kecil (three coordinated objects)

You don’t need to repeat mempunyai before each noun. This is completely normal and natural in Malay.

Why is it skrin besar, papan kekunci selesa, and tetikus kecil instead of besar skrin, selesa papan kekunci, etc.?

In Malay, adjectives almost always come after the noun:

skrin besar = big screen
papan kekunci selesa = comfortable keyboard
tetikus kecil = small mouse

This is the usual order:

noun + adjective
- baju baru (new shirt)
- kereta mahal (expensive car)
- rumah besar (big house)

Putting the adjective before the noun, like besar skrin, is generally ungrammatical or would sound very marked/poetic. So stick to noun first, adjective after.

There’s no “a” or “the” in the Malay sentence. How do I know if it’s “a big screen” or “the big screen”?

Malay generally does not use articles like a/an/the.

The phrase skrin besar could be translated as:

a big screen, the big screen, or just big screen(s)

Which one you choose in English depends on context, not on any word in the Malay sentence.

To be more specific in Malay, you can add extra words:

sebuah skrin besar = a big screen (one unit, somewhat specific)
skrin besar itu = that big screen / the big screen
beberapa skrin besar = several big screens

But in many normal sentences, Malay just omits articles and lets context do the work.

Does the sentence mean one keyboard and one mouse, or could it be plural?

As written, Malay does not explicitly mark plural:

skrin besar = big screen / big screens
papan kekunci selesa = comfortable keyboard / comfortable keyboards
tetikus kecil = small mouse / small mice

We normally assume singular here because:

It’s a single computer, and
A computer typically has one screen, one keyboard, one mouse.

If you really want to show plural, you can add a quantity word or a plural marker:

banyak skrin besar = many big screens
dua papan kekunci selesa = two comfortable keyboards
beberapa tetikus kecil = several small mice

But the base forms are neutral for number.

What does papan kekunci literally mean, and is it always two words?

Literally:

papan = board / plank
kekunci = keys (as in keyboard keys)

So papan kekunci = keyboard (a board of keys).

Notes:

It is normally written as two words: papan kekunci.
You don’t usually say papan kunci; kekunci is the standard form here.
In casual speech, some people might just say keyboard, borrowing the English word, especially in informal contexts.

In standard Malay, especially in writing, papan kekunci is the correct and common term.

Is tetikus the normal word for a computer mouse? It looks like “little mouse”.

Yes, tetikus is the standard Malay word for a computer mouse.

It’s formed from tikus (mouse) with the prefix te- / te-…-kus pattern, creating a specific technical term.
It functions just like a regular noun:
- tetikus kecil = small mouse
- tetikus tanpa wayar = wireless mouse

You may also hear mouse used directly (borrowing from English), but in formal or neutral Malay, tetikus is the preferred term.

Is the word order at the beginning, Di meja belajar, komputer saya..., the only option? Could I say it another way?

You can change the order slightly while keeping the meaning. The current sentence:

Di meja belajar, komputer saya mempunyai skrin besar, papan kekunci selesa, dan tetikus kecil.
= On/At the study desk, my computer has a big screen, a comfortable keyboard, and a small mouse.

Alternative structures:

Komputer saya di meja belajar mempunyai skrin besar, papan kekunci selesa, dan tetikus kecil.
- My computer on the study desk has a big screen…
Di meja belajar saya, terdapat sebuah komputer dengan skrin besar, papan kekunci selesa, dan tetikus kecil.
- On my study desk, there is a computer with a big screen, a comfortable keyboard, and a small mouse.
- Here, terdapat means there is/are, and dengan links the computer to its features.

Your original sentence is natural and correct; these are just stylistic variants.

Can I drop mempunyai and just list the items, like Komputer saya, skrin besar, papan kekunci selesa, dan tetikus kecil?

No, you cannot simply drop mempunyai and keep the same meaning.

Komputer saya, skrin besar, papan kekunci selesa, dan tetikus kecil
sounds like a list of four separate things, not “my computer has…”.

Malay normally needs a verb to express the relationship “X has Y”:

Komputer saya mempunyai skrin besar… (formal/neutral)
Komputer saya ada skrin besar… (more casual)

Without mempunyai/ada, the sentence becomes unclear or ungrammatical as a full statement.