Learn Hardcore Malay: Visa saya sudah diluluskan semalam.

it is still correct and still understood as past (because of semalam = yesterday).
Sudah just emphasizes the state of completion: it’s done, finished.

So:

With sudah: slight emphasis on “already / has been”.
Without sudah: neutral statement about a past event.

What is the function of the prefix di- in diluluskan?

The prefix di- marks the passive voice in Malay.

meluluskan = to approve (active)
diluluskan = to be approved (passive)

So:

Mereka meluluskan visa saya semalam.
= They approved my visa yesterday. (active)
Visa saya sudah diluluskan semalam.
= My visa was approved yesterday. (passive)

In the original sentence, the visa is the thing receiving the action, so di- is used.

What is the -kan at the end of diluluskan doing?

Base word: lulus = to pass / be approved.

The suffix -kan often makes a verb causative or transitive (“cause something to be X / do X to something”).

lulus (intransitive):
Permohonan itu lulus. = The application passed / was approved.
meluluskan sesuatu (transitive): to approve something
Mereka meluluskan permohonan saya. = They approved my application.
diluluskan (passive of the transitive verb):
Permohonan saya telah diluluskan. = My application has been approved.

So di- + lulus + -kan = diluluskan “to be approved (something is approved)”.

Is diluluskan a past tense form?

Malay verbs do not change form for tense (past/present/future).
Diluluskan is just passive voice; it has no tense by itself.

Tense/aspect is shown by:

Time words: semalam (yesterday), esok (tomorrow), etc.
Aspect markers: sudah, telah, akan, sedang, etc.

So diluluskan could mean:

is being approved
was approved
will be approved

The sentence Visa saya sudah diluluskan semalam is past because of:

sudah (already, completed)
semalam (yesterday)

What is the difference between sudah and telah here?

Both sudah and telah indicate completed action (“already / has/have”).

Visa saya sudah diluluskan semalam.
Visa saya telah diluluskan semalam.

Meaning: essentially the same.

Differences:

sudah: very common in speech and writing, neutral.
telah: more formal / written, e.g. official letters, news reports.

In everyday conversation, sudah is more natural. In a formal letter from the immigration office, telah is very likely.

Can I say Visa saya lulus semalam instead? Is that correct?

Yes, Visa saya lulus semalam is grammatically correct and understandable.

Nuance:

Visa saya lulus semalam.
Literally “My visa passed yesterday.”
More casual, more like saying “My visa passed” or “My application passed”.
Visa saya sudah diluluskan semalam.
Passive, more formal-feeling, and explicitly about the approval action.

Both are fine; in everyday talk, Visa saya dah lulus semalam (using dah for sudah) is very common.

Why is semalam at the end? Can I move it?

Time expressions like semalam (yesterday) are quite flexible in Malay.

All of these are acceptable:

Visa saya sudah diluluskan semalam.
Semalam visa saya sudah diluluskan.
Visa saya semalam sudah diluluskan. (less common, but still heard)

Most natural/common:

Beginning or end of the sentence: 1 and 2.

Choosing position:

At the end (original sentence): feels neutral.
At the beginning: slightly emphasizes the time (“As for yesterday, my visa was approved.”).

Do I need to say who approved the visa? How do I add the agent?

You don’t have to mention the agent in Malay passives; often it’s obvious.

If you want to specify the agent, you usually use oleh (by):

Visa saya sudah diluluskan oleh imigresen semalam.
= My visa was approved by immigration yesterday.

You can replace imigresen with any relevant noun:

oleh pegawai imigresen (by the immigration officer)
oleh universiti (by the university)

Why is it Visa saya, not Saya punya visa?

Both exist, but they differ in style:

Visa saya = standard, neutral, and preferred in normal Malay.
Saya punya visa = literally “my one visa”, more colloquial, often heard in informal speech, especially in some dialects.

So:

Formal / standard: Visa saya sudah diluluskan semalam.
Very informal spoken: Saya punya visa dah lulus semalam.

Can I use aku instead of saya here?

Grammatically yes:

Visa aku sudah diluluskan semalam.

But aku is:

Casual, intimate, often used with friends/family or in informal contexts.
Inappropriate or rude in many formal/professional situations.

Saya is:

Polite, neutral, safe in almost all contexts.

So use:

saya in anything formal or with strangers.
aku only where it is socially appropriate.

Is there any classifier needed with visa, like sehelai visa or satu visa?

With visa, classifiers are usually not used in everyday Malay.

You normally say:

Visa saya (my visa)
Dua visa pelancong (two tourist visas)

If you really want to emphasize the count, you can use satu:

Satu visa saya sudah diluluskan semalam.
(sounds a bit unnatural unless there’s a contrast, like “one of my visas…”)

Classifiers like sehelai, sebuah, etc. are used with many nouns, but visa typically doesn’t need one in common usage.

How would I say the same idea in an active sentence instead of passive?

Active voice: use meluluskan and put the approver as the subject.

Examples:

Imigresen sudah meluluskan visa saya semalam.
= Immigration already approved my visa yesterday.
Mereka meluluskan visa saya semalam.
= They approved my visa yesterday.

Structure:

[Agent] + (sudah/telah) meluluskan + [object] + [time].

This contrasts with the passive:

Visa saya sudah diluluskan (oleh mereka) semalam.