Learn Hardcore Hausa: Matashiya ta yi tafiye-tafiye zuwa manyan laburare domin ta yi bincike na musamman. - The young woman made trips to big libraries in order to do special research.

The basic word is matashi = young person / youth (usually male or generic).
matashiya is the specifically feminine form, so it refers to a girl or young woman.
If you wanted a male, you would say matashi; for young people in general (mixed group), you’d normally use the plural matasa.

Why is the pronoun ta used, not ya?

Hausa verbs agree with the subject in gender and number.

ta is the 3rd person singular feminine subject pronoun (“she”).
ya is the 3rd person singular masculine subject pronoun (“he”).

Because matashiya is grammatically feminine, the verb takes ta:

Matashi ya yi… (A young man did…)
Matashiya ta yi… (A young woman did…)

What is going on with ta yi tafiye-tafiye? Why is tafiyā doubled like that?

Tafiya means “a trip / a journey”. When you reduplicate it as tafiye-tafiye, it usually means:

multiple trips (plural), and often
repeated or frequent traveling.

So ta yi tafiya = “she made a trip / she traveled (once)”,
while ta yi tafiye-tafiye suggests “she has been doing a lot of traveling / several trips.”

Is ta yi a tense marker here? What tense or aspect does it express?

Yes. In ta yi, the pattern subject pronoun + yi is the perfective (completed action) form.
So ta yi tafiye-tafiye is best understood as “she made trips / she has (already) done some traveling,” focusing on the fact that the traveling is a completed or established fact, not something ongoing or habitual right now.

Why do we repeat ta yi: …ta yi tafiye-tafiye… domin ta yi bincike…? Could we skip the second ta yi?

You normally repeat the subject pronoun and verb after domin when the same subject is performing a new, clear action.

…ta yi tafiye-tafiye… domin ta yi bincike… literally: “she made trips in order that she should do research…”

You could restructure it as:

…zuwa manyan laburare domin yin bincike na musamman.
Here yin is a verbal noun (“the doing of research”), and you don’t need to repeat ta. But in the original structure, repeating ta yi is natural and clear.

What does domin mean here, and how is it different from don or saboda?

Domin here introduces a purpose: “in order to / so that / for the purpose of”.

domin ta yi bincike = “in order for her to do research / so that she can do research.”

don is basically a shorter, more colloquial form often used like domin, especially in speech.
saboda usually means “because” (reason) rather than “in order to” (purpose), though in some contexts it can blur a bit; here domin is the best choice because the clause expresses her goal.

How does manyan laburare work? Which part is plural and how do we know it’s “libraries”, not “library”?

Manyan is the plural form of the adjective babba (“big, important”).

Singular: babban laburare = a big / major library
Plural: manyan laburare = big / major libraries

The noun laburare itself (from “library”) often stays the same form in singular and plural, and the adjective’s form (babban vs manyan) plus context tells you whether it’s singular or plural.

What does bincike na musamman literally mean, and what is the function of na?

Bincike = research / investigation.
musamman = special, particular.
na is the linker (genitive/construct particle) that connects a noun to something describing or qualifying it.

So:

bincike na musamman literally = “research of special (type)” → “special research / specialized research”.
You use na the same way in many noun + adjective phrases, especially when the adjective comes after the noun:
aiki na gida = homework (“work of home”)
abinci na musamman = special food.

Could you say bincike musamman without na?

You might hear musamman used adverbially (e.g., “especially”), but when it directly qualifies a noun in this way, bincike na musamman is the standard, natural pattern.
Leaving out na (→ bincike musamman) sounds incomplete or unusual in formal/standard Hausa for “special research.” The na clearly marks the relationship between the noun and its descriptor.

Why do we need zuwa before manyan laburare? Could we just say …tafiye-tafiye manyan laburare?

Zuwa is the preposition “to / towards”.

ta yi tafiye-tafiye zuwa manyan laburare = “she made trips to big libraries.”

Without zuwa, manyan laburare would just look like another object or description, not a destination. You need zuwa here to show direction or goal of the movement, similar to the English “to” in “trips to libraries.”

How would this sentence change if the subject were a young man instead of a young woman?

You’d change the noun and the agreeing pronouns from feminine to masculine:

Matashi ya yi tafiye-tafiye zuwa manyan laburare domin ya yi bincike na musamman.

Changes:

Matashiya → Matashi (young woman → young man)
ta yi → ya yi (she did → he did), in both places, to match the masculine subject.