Learn Hardcore Hausa: Iyayensu suna ba matasa tarbiya mai kyau domin su san muradinsu a rayuwa. - Their parents give the youth good upbringing so that they know their aims in life.

Base noun: iyaye = parents
Possessive pronoun: su = they / their (3rd person plural)
When a noun ending in a vowel takes a possessive pronoun, Hausa usually inserts a linker -n-:

iyaye + -n- + su → iyayen‑su → iyayensu = their parents

So su here is a possessive pronoun (their), not the subject they.

Why do we have suna here? What does it add to the verb?

Suna is the 3rd person plural form of the aspect marker that shows continuous or habitual action.

suna ba … = they are giving / they (usually) give
Without suna, ba by itself would normally be understood as a past form if you just said sun ba … (they gave).

So Iyayensu suna ba… means their parents are giving / usually give…, not their parents gave….

The word ba can mean both "give" and be a negative marker in Hausa. How can I tell which one it is here?

In this sentence, ba is the verb meaning to give.

You can distinguish them mainly by position and pattern:

Verb "ba" (give) comes after the subject + aspect marker:
- Iyayensu suna ba matasa tarbiya… = Their parents are giving youths upbringing…
Negative "ba" normally appears:
- At the beginning of the clause, often with another ba at the end:
  - Ba su ba matasa tarbiya mai kyau ba. = They do not give youths good upbringing.

Since in our sentence ba is in the verb slot (after suna) and there is no matching ba … ba frame, it clearly means give.

Why is it ba matasa tarbiya and not ba tarbiya matasa? Which one is the recipient and which is the thing being given?

With the verb ba (to give), the normal order is:

Subject + TAM (e.g. suna) + ba + recipient (indirect object) + thing given (direct object)

So in:

suna ba matasa tarbiya mai kyau
- matasa = the recipients (the youths)
- tarbiya mai kyau = the thing given (good upbringing)

If you wanted to put the thing given first, you would normally add a preposition like ga or wa before the recipient:

suna ba tarbiya mai kyau ga matasa = they give good upbringing to the youths.

Without ga/wa, the noun right after ba is understood as the recipient.

What exactly does matasa mean, and what is its singular form?

Matasa means young people / youths (a group of young adults).

Singular: matashi = a young man / youth
Feminine singular: yarinya (girl; not from the same root, but used for young female) or matashiya in some contexts.

So matasa is a plural referring to a group of young people.

What does tarbiya mean in this context? Is it just "education"?

Tarbiya (also written tarbiyya) is a loanword from Arabic and is broader than just school education. It covers:

upbringing,
moral training,
discipline,
teaching good manners and character.

In this sentence, tarbiya mai kyau is best understood as good upbringing / good moral training, not specifically formal schooling.

How does mai kyau work in tarbiya mai kyau? Why is the adjective after the noun?

In Hausa, descriptive words normally follow the noun they describe.

Mai kyau literally means one that has goodness/beauty, and it functions as an adjective meaning good / nice / beautiful.

tarbiya mai kyau = upbringing that has goodness → good upbringing
mota mai kyau = good car

For plural nouns, mai becomes masu:

motoci masu kyau = good cars

So tarbiya mai kyau is a singular noun phrase: good upbringing.

What does domin mean here, and how does it connect the clauses?

Domin means so that / in order that / because, depending on context. Here it introduces a purpose clause:

… suna ba matasa tarbiya mai kyau domin su san …
= … they give young people good upbringing so that they know …

You can often shorten domin to don in speech:

don su san muradinsu a rayuwa

So domin links the first action (giving upbringing) to its purpose (so that the youths will know their goals).

Why is it su san and not su sani in domin su san muradinsu?

Here su san is a finite verb form in a subordinate clause:

su = they (subject pronoun)
san = verb know (finite/base form)

Sani is the verbal noun / infinitive ("knowing"), used in structures like:

son sanin gaskiya = the desire of knowing the truth.

In a clause after domin, Hausa normally uses a subject pronoun + base verb (often called the subjunctive form):

domin in tafi = so that I may go
domin su gane = so that they understand
domin su san = so that they know

So su san is the correct finite form here; su sani would sound wrong in this position.

In domin su san muradinsu, does su refer to the parents or to the youths?

Grammatically, su is just "they", and in theory it could refer to either iyayensu (their parents) or matasa (the youths).

However, by normal interpretation and logic, it refers to matasa:

The parents give good upbringing to young people,
so that they (the young people) know their goals in life.

Context and meaning make it clear that su refers to the youths, not the parents.

What does muradinsu mean, and how is it formed?

Muradinsu means their goals / their aims / their desires.

Base noun: muradi = wish, aim, goal, desire
Possessive: -n- + su = their

Formation:

muradi + -n- + su → muradin‑su → muradinsu = their goals / their aims

So muradinsu is "their goals", and in this sentence it refers to the youths’ goals.

What does a rayuwa mean, and what is the role of a?

A rayuwa means in life.

a = a general preposition, often meaning in / at / on depending on context
rayuwa = life

So:

muradinsu a rayuwa = their goals in life.

If you wanted to say in their lives more explicitly, you could say:

a rayuwarsu = in their life/lives (with -r-
- su as possessive on rayuwa).

Could you also say this sentence in another way, for example using ga or wa with matasa?

Yes, you can rephrase while keeping the same meaning. Some natural variants:

Iyayensu suna ba matasa tarbiya mai kyau domin su san muradinsu a rayuwa.
(original: give youths good upbringing)
Iyayensu suna ba tarbiya mai kyau ga matasa domin su san muradinsu a rayuwa.
(give good upbringing to youths)
Iyayensu suna ba matasa tarbiya mai kyau don su san muradinsu a rayuwa.
(uses don instead of domin)

All are acceptable; the first is very natural and compact, the second makes the "to youths" part more explicit with ga matasa.