Learn Hardcore Swahili: Wakati wa ujana, kaka yangu alinunua tiketi za bahati nasibu kila wiki. - During his youth, my brother bought lottery tickets every week.

So the phrase is “the time of youth”, which is naturally understood as “during youth / in (someone’s) youth”.
In context, because the sentence is talking about kaka yangu, it will usually be understood as “in my brother’s youth” or “when my brother was young”, even though “his” is not explicitly said.

Why is there no separate word for “in” before wakati wa ujana? Why not katika wakati wa ujana?

Swahili often expresses “in/at the time of …” simply with wakati wa … without adding katika.

wakati wa ujana = “the time of youth” → understood as “during youth / in youth”
Adding katika (katika wakati wa ujana) is not wrong, but it sounds a bit heavier and is less common in a simple sentence like this.

So wakati wa ujana on its own already carries the idea of “during / when”, and that is usually enough.

How do we know wakati wa ujana refers to my brother’s youth and not someone else’s?

Grammatically, wakati wa ujana is neutral: it just says “the time of youth”.

Swahili often relies on context to decide whose youth is meant. Since the sentence is about kaka yangu, a Swahili speaker will naturally understand it as “in my brother’s youth”.

If you need to be explicit, you can add a possessive:

wakati wa ujana wake = in his/her youth
wakati wa ujana wangu = in my youth

So a more explicit version could be:

Wakati wa ujana wake, kaka yangu alinunua …
“In his youth, my brother bought …”

Could I put wakati wa ujana at the end of the sentence instead of at the beginning?

Yes. Swahili word order is fairly flexible with time expressions. All of these are grammatical:

Wakati wa ujana, kaka yangu alinunua tiketi za bahati nasibu kila wiki.
Kaka yangu alinunua tiketi za bahati nasibu kila wiki wakati wa ujana.

Putting wakati wa ujana at the beginning gives a little extra emphasis to the time (“As for the time when he was young…”), but the basic meaning is the same.

What is the structure of kaka yangu and why is yangu placed after kaka?

kaka yangu literally means “brother my”, but in Swahili the possessive follows the noun:

kaka = brother
yangu = my

So:

kaka yangu = my brother
rafiki yangu = my friend
mwalimu wangu / mwalimu wangu (regional) = my teacher

In Swahili, the pattern is noun + possessive, so you say kaka yangu, not yangu kaka.

Why is it kaka yangu and not kaka wangu? I learned that class 1 nouns use wangu.

Your grammar rule is right in general, but some kinship terms behave irregularly.

Many common family words (like baba, mama, kaka, dada) take yangu / yako etc. instead of wangu / wako in everyday usage:

baba yangu = my father
mama yangu = my mother
kaka yangu = my brother
dada yangu = my sister

So even though they take class 1 agreement in the verb (kaka yangu alinunua…, not wanunua), with possessives you normally say yangu, not wangu. It’s something you mostly just learn by exposure.

What exactly is inside the verb alinunua?

alinunua breaks down as:

a- = subject marker “he/she” (third person singular)
-li- = past tense marker (simple past)
-nunua = verb root “buy”

So a + li + nunua → alinunua = “he bought”.

Because the sentence has kila wiki (“every week”), this simple past is understood as “used to buy / would buy (repeatedly)” in English.

If I want to say “used to buy” more clearly (past habit), is alinunua enough, or should I use another tense?

Alinunua with a time expression like kila wiki is absolutely natural for a repeated past action. Context gives it the “used to” feeling.

If you want to emphasize the idea of an ongoing habit, you have options like:

Kaka yangu alikuwa akinunua tiketi za bahati nasibu kila wiki.
“My brother used to be buying / was in the habit of buying lottery tickets every week.”

Here:

alikuwa = he was
akinunua = buying (continuous aspect)

But in everyday speech, alinunua … kila wiki is already perfectly fine for “used to buy every week”.

Why doesn’t tiketi change form in the plural? Shouldn’t there be a plural prefix?

Tiketi is a loanword (from English “ticket”) that belongs to the so‑called N class (class 9/10). Many nouns in this class have the same form in singular and plural.

Examples:

tiketi moja = one ticket
tiketi nyingi = many tickets
siku moja = one day
siku nyingi = many days

So tiketi can mean “ticket” or “tickets”; the number is shown by context or by words like moja, mbili, nyingi, kila, etc.

What does za do in tiketi za bahati nasibu, and why is it za instead of wa?

za is the -a connector meaning “of”, and it agrees with the noun class of tiketi.

tiketi is in the N class (class 10 here), whose -a form is za.
So tiketi za bahati nasibu = “tickets of lottery” → lottery tickets.

Different noun classes use different forms of -a:

class 1: wa (e.g. mtoto wa jirani – the neighbor’s child)
class 10: za (e.g. tiketi za bahati nasibu – lottery tickets)

So we get tiketi za …, not tiketi wa ….

Is bahati nasibu just one word meaning “lottery,” or do bahati and nasibu each mean something?

Bahati nasibu is a fixed expression meaning “lottery / raffle”.

Individually:

bahati = luck, good fortune
nasibu = chance, randomness

Together, bahati nasibu is understood as “a game of chance”, i.e., a lottery.
So tiketi za bahati nasibu = lottery tickets.

Why is it kila wiki (“every week”) and not something like kila wiki moja or a plural form?

Kila always goes with a singular noun in Swahili, even though the meaning is “every (plural set)”:

kila siku = every day
kila mwezi = every month
kila wiki = every week

You do not pluralize the noun (kila wiki is correct, not kila wiki nyingi), and you normally don’t add moja here. The idea of “each one individually” is already contained in kila.