Learn Hardcore Malay: Saya daftar akaun baru di aplikasi bank untuk melihat simpanan saya. - I register a new account in the banking app to see my savings.

Saya mendaftar akaun baru… is more standard / formal and is what textbooks usually teach.
Saya daftar akaun baru… is very common in casual spoken Malay. The meN- prefix is often dropped in everyday speech, especially with common verbs like daftar, beli, call, check.

So:

Formal/written: Saya mendaftar akaun baru di aplikasi bank…
Informal/spoken: Saya daftar akaun baru kat/di app bank…

Is daftar here past tense (“I registered”) or present (“I am registering”)? How does Malay show tense?

Malay verbs don’t change form for tense. Daftar can mean:

I registered (past)
I am registering (present)
I will register (future)

If you need to be explicit, you add time words:

Past: Saya sudah / telah daftar akaun baru… (I already registered…)
Present (right now): Saya sedang daftar akaun baru… (I am in the middle of registering…)
Future: Saya akan daftar akaun baru… (I will register…)

In your sentence, context decides whether it’s past or present.

Why is it akaun baru and not baru akaun? What is the normal adjective order?

In Malay, adjectives usually come after the noun:

akaun baru = new account
kereta besar = big car
telefon lama = old phone

So:

Noun + adjective

Baru akaun is wrong in standard Malay for “new account”. It would sound ungrammatical or at best very odd.

Do I really need akaun and bank together? What is the difference between akaun, akaun bank, and just akaun baru?

akaun = account (general)
akaun bank = bank account (more specific)
akaun baru = new account (could be a bank app account, an email account, etc.)

Your sentence akaun baru di aplikasi bank suggests:

a new account within the bank’s app, not necessarily a new bank account at a branch.

If you want to be very clear that it is a bank account:

Saya daftar akaun bank baru di aplikasi bank… (I opened a new bank account in the banking app…)

Is di aplikasi bank the most natural way to say “on the banking app”? Could I use dalam, pada, or melalui instead?

Di aplikasi bank is understandable and fine, especially in speech.

Other options:

melalui aplikasi bank = through the banking app (very natural and common)
dalam aplikasi bank = inside the banking app (focus on “inside”)
pada aplikasi bank is grammatically possible but sounds less natural here than di or melalui.

So you could say:

Saya daftar akaun baru melalui aplikasi bank…
which is a very natural alternative.

What does untuk melihat mean literally, and why do we need untuk before melihat?

untuk = for / in order to
melihat = to see / to look at

So untuk melihat = “in order to see / to see (for the purpose of seeing)”.

In your sentence, it introduces the purpose:

…di aplikasi bank untuk melihat simpanan saya.
= “…in the banking app to see my savings.”

Without untuk, melihat simpanan saya would feel more like a second action than a purpose clause.

What is the difference between lihat, melihat, and tengok?

They are all related to “see/look”, but with different levels of formality:

melihat
- More formal, standard.
- Common in writing, news, formal speech.
lihat
- Base form; can appear in certain structures or more neutral/informal usage.
- Often used in commands: Lihat sini. (Look here.)
tengok
- Very informal / colloquial.
- Common in everyday spoken Malay: Saya nak tengok simpanan saya.

For an informal version of your sentence:

Saya daftar akaun baru di app bank nak tengok simpanan saya.

What does simpanan mean exactly? How is it different from duit, wang, or baki?

simpanan
- from simpan (to keep/save)
- means savings (money that has been put aside/kept)
duit / wang
- both mean money (duit is more common in everyday speech; wang is more formal).
baki
- balance / remaining amount (e.g. account balance, change after paying)

So:

melihat simpanan saya = looking at my savings (overall money saved)
melihat baki akaun saya = looking at my account balance

Why do we repeat saya at the end (simpanan saya)? Can we just say simpanan?

Simpanan by itself just means “savings” in general.

To show possession (“my savings”), you add a possessive pronoun:

simpanan saya = my savings
simpanan awak = your savings
simpanan dia = his/her savings

You could also use the suffix -ku in more literary or expressive style:

simpanan ku (often written simpanan ku or simpananku) = my savings

Leaving it as only simpanan would usually be understood as savings in general, not necessarily yours.

Can I drop Saya and just say Daftar akaun baru di aplikasi bank untuk melihat simpanan saya?

In a full sentence in standard Malay, you normally keep Saya:

Saya daftar akaun baru…

However, in:

notes
app interfaces
instructions
dropping Saya is common, because the subject is understood:
Daftar akaun baru di aplikasi bank untuk melihat simpanan anda.
(Register a new account on the banking app to see your savings.)

So for normal conversation: keep Saya.
For headings/instructions: you can drop it.

How would I make this sentence more formal, like for writing to a bank?

You can:

Use mendaftar instead of daftar
Add a past marker like telah (if it’s already done)
Use more formal choices for some words

Example:

Saya telah mendaftar akaun bank yang baharu melalui aplikasi bank untuk menyemak simpanan saya.

Changes:

telah mendaftar = have registered
akaun bank yang baharu = more formal phrase for “new bank account”
melalui aplikasi bank instead of di aplikasi bank
menyemak (to check) instead of melihat, if you mean “check” rather than just “see”

Is akaun always spelled like that in Malay, even though English has account?

Yes, in standard Malay the correct spelling is:

akaun (not account, akun, or akaunt)

Malay borrows many words from English but adjusts the spelling to Malay phonetics and orthography, so you will see akaun in official documents, bank websites, and exams.