Zipu ya koti lako iko wazi, na kola ya blauzi yako imekunjika.

Because the zi- in zipu is just part of the word, not a plural prefix.

Zipu is normally treated as a singular class 9 noun here, so it takes singular agreement: iko.
If you were talking about more than one zipper, the noun might still look the same, but the agreement would change:

zipu iko wazi = the zipper is open
zipu ziko wazi = the zippers are open

So in many Swahili nouns, especially loanwords, agreement tells you the number more clearly than the noun’s shape does.

Here ya means of.

So:

zipu ya koti lako = the zipper of your coat
kola ya blauzi yako = the collar of your blouse

This is a very common Swahili pattern: noun + linker + noun.
English often prefers your coat’s zipper, but Swahili usually expresses it as zipper of your coat.

Because possessives in Swahili agree with the noun class of the noun they describe.

• koti is treated as a class 5 noun, so your becomes lako
• blauzi is treated as a class 9 noun, so your becomes yako

So:

koti lako = your coat
blauzi yako = your blouse

This is one of the big differences from English: Swahili possessives change form depending on the noun class.

That is the normal Swahili word order.

In English, you say your coat.
In Swahili, you say koti lako, literally coat your.

The same pattern appears throughout the sentence:

koti lako = your coat
blauzi yako = your blouse

So for learners, it helps to get used to this pattern early: noun first, possessive second.

Because lako comes directly after koti.

So:

zipu ya koti lako means the zipper of your coat

The possessive lako modifies koti, not zipu.

If you wanted to say your zipper, you would say:

zipu yako

So position matters a lot here.

Iko wazi is a natural way to describe the current physical state of something: it is open.

Here, iko agrees with zipu and works well for a present state:

zipu ... iko wazi = the zipper is open

You may also see ni wazi in other contexts, but iko wazi sounds especially natural when talking about a thing’s actual condition or position at the moment.

Iko is made up of:

• i- = the subject marker for a singular class 9 noun
• -ko = a form used for being in a state or place

Since zipu is class 9 singular, the sentence uses iko.

So iko wazi is basically it is open, with it built into the verb form.

This is why Swahili often does not need a separate word for it.

Imekunjika can be broken down like this:

• i- = subject marker for class 9 singular, agreeing with kola
• -me- = perfect aspect, often meaning has or a resulting current state
• kunj- = the root from kunja, meaning fold or bend
• -ika = a stative/intransitive ending, giving the sense become folded/bent

So imekunjika means something like:

• has become folded
• is folded over
• has gotten bent/creased

In this sentence, it describes the collar’s condition.

These two forms are close, but they are not exactly the same.

• imekunjika focuses on the resulting state: it has become folded/bent
• imekunjwa is passive: it has been folded

For a collar that is sitting wrong, turned over, or creased, imekunjika is very natural because it describes the condition the collar is in, not necessarily the action done by someone.

Na means and.

It joins the two parts of the sentence:

• Zipu ya koti lako iko wazi
• kola ya blauzi yako imekunjika

So the whole sentence says two things about the person’s clothes and links them with na.

Because Swahili usually does not use articles like the and a/an.

So zipu can mean:

• the zipper
• a zipper

and context tells you which one is meant.

In this sentence, the context makes it definite, so English naturally translates it with the.

Yes, they are loanwords or loanword-like forms, and English speakers often recognize them:

• zipu ≈ zipper / zip
• koti ≈ coat
• kola ≈ collar
• blauzi ≈ blouse

That can make vocabulary easier to remember. But even though they are borrowed words, they still follow Swahili grammar, including noun-class agreement such as iko, yako, and lako.