Bu sabah bir kivi yedim; kuzenim ananas istedi.

Because Turkish normally uses Subject–Object–Verb order.

So in:

• bir kivi yedim = a kiwi I-ate
• kuzenim ananas istedi = my cousin pineapple wanted

Putting the verb at the end is the most neutral and common pattern in Turkish.
English usually puts the verb earlier, but Turkish prefers to save it for the end of the clause.

Bu sabah is a time expression meaning this morning.

• bu = this
• sabah = morning

Together they act like one time phrase. Turkish does not need a preposition here, so there is no word for in. English says this morning, and Turkish also simply says bu sabah.

Bir usually means one or a/an.

So:

• bir kivi yedim = I ate a kiwi

Using bir makes the noun clearly singular and indefinite.
If you just said kivi yedim, it could still be natural in some contexts, but bir kivi is a very straightforward way to say a kiwi.

In Turkish, indefinite direct objects often have no accusative ending.

So:

• bir kivi yedim = I ate a kiwi
• kiviyi yedim = I ate the / that specific kiwi

The form kiviyi uses the accusative because it refers to a specific, identifiable kiwi.
In your sentence, bir kivi is indefinite, so no accusative is used.

For the same reason: it is being treated as an indefinite object.

• ananas istedi = wanted pineapple / some pineapple
• ananası istedi = wanted the pineapple / that specific pineapple

So the lack of accusative tells you the object is non-specific or indefinite.

Because ananas here can be understood more generally as pineapple rather than one whole pineapple.

Compare:

• ananas istedi = wanted pineapple / wanted some pineapple
• bir ananas istedi = wanted a pineapple / wanted one pineapple

Both are possible, but they mean slightly different things.
Without bir, it sounds more like the person wanted the food item in general.

Yedim comes from the verb yemek = to eat.

It breaks down like this:

• verb stem: ye-
• past tense: -di
• 1st person singular: -m

So:

• ye + di + m → yedim = I ate

This is the simple past tense.

İstedi comes from istemek = to want.

It breaks down like this:

• stem: iste-
• past tense: -di

So:

• iste + di → istedi = he/she wanted

In Turkish, third person singular often has no extra personal ending in the past tense beyond the tense marker itself.

Because the ending -im is a possessive suffix meaning my.

• kuzen = cousin
• kuzenim = my cousin

Turkish usually attaches possession directly to the noun instead of using a separate word like my every time.

You can also say benim kuzenim, but that adds emphasis or clarity:

• kuzenim = my cousin
• benim kuzenim = my cousin, with extra emphasis on my

Because Turkish verbs often already show who is doing the action.

• yedim already means I ate

The -m ending tells you the subject is I, so a separate pronoun ben is not necessary.

Turkish often leaves subject pronouns out unless they are needed for emphasis or contrast.

Yes. You could say:

• Bu sabah ben bir kivi yedim; kuzenim ananas istedi.

That would still be correct, but ben adds emphasis, something like:

• I ate a kiwi this morning; my cousin wanted pineapple.

Without ben, the sentence is more neutral and natural in many contexts.

The suffix -di marks the simple past, often used for completed actions.

In this sentence:

• yedim = I ate
• istedi = he/she wanted

It tells you both actions happened in the past.
This is one of the most common Turkish past tense forms.

Yes, Turkish does use vowel harmony, and the past tense suffix can appear as:

• -dı
• -di
• -du
• -dü and also with t instead of d after certain sounds:
• -tı, -ti, -tu, -tü

Here it is -di because the vowel harmony matches the preceding vowels in ye- and iste-.

So:

• ye + di + m → yedim
• iste + di → istedi

Yes. Turkish word order is flexible, especially for time expressions.

For example:

• Bu sabah bir kivi yedim.
• Bir kivi bu sabah yedim.
• Bir kivi yedim bu sabah.

These are all possible, though the first one is the most neutral here.
Changing the order can shift focus or emphasis.

The semicolon links two related independent clauses:

• Bu sabah bir kivi yedim
• kuzenim ananas istedi

It works much like in English: it shows a close connection between two complete thoughts without using a conjunction like and or but.

It is punctuation, not a special Turkish grammar rule.

Yes, you could say:

• Bu sabah bir kivi yedim ve kuzenim ananas istedi.

That means I ate a kiwi this morning and my cousin wanted pineapple.

However, the semicolon gives a slightly more separated, written feel.
Using ve makes the connection more explicit.

Not in this sentence, but if you wanted plurals:

• kiviler = kiwis
• ananaslar = pineapples

Turkish plural is usually formed with -ler / -lar depending on vowel harmony.

But since the sentence refers to singular or uncounted food, the singular forms are used:

• kivi
• ananas