Learn Hardcore Swahili: Kesho dada yangu atavaa sketi ndefu na koti jeupe kwenda kazini. - Tomorrow my sister will wear a long skirt and a white jacket to go to work.

Dada belongs to noun class 9 (it doesn’t start with m- or ki-, etc.; its plural is also dada).
The class‑9 form of “my” is yangu, not wangu.

So:

dada yangu = my sister
mtoto wangu = my child (class 1, which uses wangu)

Some kinship words take wangu (e.g. mtoto wangu, mjomba wangu), but dada uses yangu because of its noun class.

Why do the adjectives come after the nouns, like sketi ndefu and koti jeupe, instead of before them?

In Swahili, adjectives normally follow the noun:

sketi ndefu = long skirt
koti jeupe = white coat/jacket
mtu mrefu = tall person
nyumba ndogo = small house

So you say sketi ndefu, not ndefu sketi.
If you put the adjective first, it sounds wrong or at least very marked in standard Swahili.

Why is it sketi ndefu and not something like sketi refu?

The basic adjective is -refu (long). It changes form depending on the noun class:

class 1 (mtu): mtu mrefu – tall/long person
class 3 (mti): mti mrefu – tall tree
class 9 (nyumba): nyumba ndefu – long/tall house

Sketi (skirt) is treated as a class‑9 noun (its plural is usually also sketi), so -refu takes the class‑9 form ndefu:

sketi ndefu = long skirt

So sketi refu would be incorrect; it must show agreement: ndefu with class 9.

Why is it koti jeupe and not koti nyeupe?

The basic adjective is -eupe (white). Like other adjectives, it changes with noun class:

class 1 (mtu): mtu mweupe – a white/light‑skinned person
class 7 (kitu): kitu cheupe – a white thing
class 9 (nyumba): nyumba nyeupe – a white house
class 5 (tunda): tunda jeupe – a white fruit

Koti (coat/jacket) is a class‑5/6 noun (singular koti, plural makoti), so -eupe takes the class‑5 form jeupe:

koti jeupe = white coat/jacket

If the noun were class 9, then nyeupe would be right, but for koti you need jeupe.

What is the role of na in sketi ndefu na koti jeupe?

Na means and when used between nouns or noun phrases:

sketi ndefu na koti jeupe = a long skirt and a white coat
chai na kahawa = tea and coffee
mama na baba = mother and father

Here it links two separate things she will wear:

sketi ndefu (long skirt)
koti jeupe (white coat)

What does kwenda mean here, and why is it kwenda and not kuenda or enda?

The verb kwenda is the infinitive form of -enda (to go).

Normally, infinitives in Swahili are formed with ku- + verb stem:

kusoma = to read
kucheza = to play
kuwa = to be

With -enda, ku- changes to kw-, so:

ku-
- enda → kwenda = to go

In your sentence, kwenda kazini means to go to work and expresses purpose:

… atavaa sketi ndefu na koti jeupe kwenda kazini.
= She will wear a long skirt and a white coat (in order) to go to work.

Using just enda here would be wrong; after another verb you need the infinitive kwenda.

What is the difference between kazi and kazini?

Kazi is the basic noun work / job.
Adding -ni makes a locative form, meaning at / in / to that place or activity:

kazini = at work / to work / in (the state of) working

So:

Niko kazini. = I am at work.
Anaenda kazini. = He/She is going to work.

In your sentence, kwenda kazini is a standard phrase meaning to go to work.
Saying kwenda kazi would sound ungrammatical; -ni is needed here.

Why is the verb marked with a- (in atavaa) instead of directly using dada yangu as the subject without any prefix?

In Swahili, the subject is normally marked twice:

As a full noun phrase: dada yangu (my sister)
As a subject marker on the verb: a- (she)

So:

Dada yangu atavaa …
dada yangu = my sister (full noun)
a- in atavaa = she (agrees with dada yangu)

You could also drop the noun and just say:

Atavaa sketi ndefu … = She will wear a long skirt …

The a- on the verb is compulsory; the full noun dada yangu is optional and used for clarity or emphasis.

Can the word order around kesho change without changing the meaning?

Yes. All of these are acceptable and mean the same thing:

Kesho dada yangu atavaa sketi ndefu na koti jeupe kwenda kazini.
Dada yangu kesho atavaa sketi ndefu na koti jeupe kwenda kazini.
Dada yangu atavaa sketi ndefu na koti jeupe kesho kwenda kazini. (a bit less common)
Dada yangu atavaa kesho sketi ndefu na koti jeupe kwenda kazini. (emphasises tomorrow)

The most neutral and common is with Kesho at the beginning.