Learn Hardcore Hausa: Malami ya koya mana cewa bambancin kuɗi bai kamata ya hana girmamawa ba. - The teacher taught us that a difference in money should not prevent respect.

Ya is the 3rd person masculine singular subject pronoun plus a perfective marker.
In ya koya, it marks that the action “teach” is completed, so in this context it corresponds to a simple past in English: “The teacher taught us…”.
Hausa always needs this kind of subject marker in a finite clause; you cannot just say Malami koya mana without ya.

What exactly is mana, and how is it different from mu or muna?

Mana is an object pronoun meaning “to us / for us”.
So ya koya mana = “he taught (it) to us.”

mu = independent pronoun “we / us” (e.g. mu ne, mu muna zuwa).
muna = “we are …ing” (1st person plural imperfective marker).
mana is specifically an enclitic indirect object: ga mu → mana (“to us”).

What does cewa do in this sentence, and can it be left out like English “that”?

Cewa is a complementizer meaning “that”, introducing a subordinate clause:

Malami ya koya mana cewa …
“The teacher taught us that …”

It links the verb koya (teach) to the content of what was taught.
Unlike English, Hausa usually needs cewa here; leaving it out (Malami ya koya mana bambancin kuɗi…) sounds wrong or at best very informal and odd.

What does bambancin kuɗi really mean? Is it just “money difference”?

Bambanci means “difference / distinction”, and bambancin kuɗi is “difference in money / financial difference”.

bambanci
- -n → bambancin (“the difference of …”)
kuɗi = money

Together it usually implies things like differences in wealth, income level, economic class, not just “two amounts of money that are not the same.”

Why is there another ya in bai kamata ya hana girmamawa ba? What does this second ya refer to?

The second ya is again a 3rd person singular subject marker, this time for the verb hana (“prevent”).
Its subject is bambancin kuɗi:

bambancin kuɗi (subject)
ya hana = “it prevents”

So literally: “the difference in money should not (be something that) prevents respect.”
Hausa repeats the subject marker like this even when the noun phrase has already been mentioned.

How does the negative structure bai … ba work in this sentence?

Bai … ba is a common way to form a negative perfective with a 3rd person singular subject:

ya hana = “he/it prevented”
bai hana ba = “he/it did not prevent”

In bai kamata ya hana girmamawa ba, the bai … ba negation wraps around kamata and the clause that follows it.
Idiomatically bai kamata … ba means “it should not / it ought not to”, even though literally it’s more like “it doesn’t be-fittingly (do X)”.

What does kamata mean by itself, and why does bai kamata … ba translate as “should not”?

Kamata on its own means something like “fittingness, propriety”, i.e. what is proper or appropriate.
In expressions like:

ya kamata ya yi haka = “he should do so / it is fitting that he do so”
bai kamata ya yi haka ba = “he should not do so / it is not fitting that he do so”

So bai kamata … ba is the standard way to say “should not / ought not to” in Hausa.

How does the verb hana work? What is the pattern for “prevent X from doing Y” in Hausa?

Hana means “to prevent / to stop / to forbid”.
The common pattern is:

hana [somebody/something] [verbal noun or action]

In this sentence, the subject is bambancin kuɗi, and the thing being prevented is girmamawa (respect):

bambancin kuɗi ya hana girmamawa
“the difference in money prevents respect”

If you specify who is being prevented, it can look like:

Ya hana mu tafiya = “He prevented us from going.”

What is girmamawa, and how is it related to the verb girmama?

Girmama is the verb “to respect, to honor”.
Girmamawa is its verbal noun / noun of action, meaning “respect, honoring” as a thing or process.

Formation:

girmama (verb) → girmamawa (verbal noun)

So ya hana girmamawa literally means “it prevents respect (from happening)”.

Why is it Malami here and not Malamin? Could we also say Malamin ya koya mana …?

Yes, you could say Malamin ya koya mana …, and that would mean “the teacher taught us …” with a definite, specific teacher.

Malami = “a teacher / teacher (in general)”
Malamin (malami + -n) = “the teacher” (a particular one already known in context)

Using Malami without -n can sound more general: “A teacher taught us that…” or “The teacher (as a role/type) taught us that…” depending on context.

Is kuɗi singular or plural, and can it also mean “wealth” or only “money”?

Historically kuɗi is a plural form, but in modern usage it typically behaves like a mass noun meaning “money” in general.
It can also extend to mean “wealth / funds / financial means”, depending on context.
You don’t usually need a separate word for “moneys”; kuɗi already covers that idea.

Are there any pronunciation or spelling details I should notice, like the hooked ɗ in kuɗi?

Yes:

The letter ɗ represents an implosive ‘d’ sound in Hausa, different from plain d. It’s important because it distinguishes words (e.g. da vs ɗa).
In kuɗi, that ɗ should be pronounced with a slight inward movement of air; English has no exact equivalent, but using a clear d is usually understood.
Make sure not to write kudi without the hook if you’re typing Hausa carefully; kuɗi is the standard orthography.