Kahvaltıda bir portakal yedim.

Because -da / -de / -ta / -te is the locative ending, which often means in, at, on.

• kahvaltı = breakfast
• kahvaltıda = at breakfast / during breakfast

The exact form changes because of vowel harmony and consonant voicing rules:

• kahvaltı ends in the vowel ı, so the suffix vowel becomes a
• the final consonant in the suffix is d here, giving -da

So kahvaltıda means at breakfast.

Bir can mean one, but it also often works like a/an in English.

So:

• bir portakal = an orange / one orange

In this sentence, it most naturally means an orange, not necessarily emphasizing the number. But depending on context, it could also stress one orange.

This is about the accusative case.

In Turkish, a direct object is often:

• without accusative if it is indefinite / non-specific
• with accusative if it is definite / specific

So:

• bir portakal yedim = I ate an orange / some unspecified orange
• bir portakalı yedim = I ate the/that one orange / a specific orange

In your sentence, the orange is just being introduced as an indefinite object, so portakal stays without the accusative ending.

Yedim comes from the verb yemek, meaning to eat.

It breaks down like this:

• ye- = verb stem (eat)
• -di = past tense
• -m = I

So yedim means I ate.

You may also see this explained as stemming from ye rather than the dictionary form yemek. Turkish dictionary forms usually end in -mek / -mak, but that ending is removed when making normal finite verb forms.

Because Turkish usually does not need subject pronouns when the verb already shows the person.

Here:

• yedim already means I ate
• the -m ending tells you the subject is I

So Ben kahvaltıda bir portakal yedim is possible, but ben is usually only added for emphasis, contrast, or clarity.

For example:

• Ben yedim, o yemedi. = I ate, he/she didn’t.

Yes, Turkish word order is flexible, but the most neutral pattern is often:

• time/place + object + verb

So this sentence is very natural:

• Kahvaltıda bir portakal yedim.

The verb commonly comes at the end in Turkish.

Other orders are possible, but they change the emphasis:

• Bir portakal kahvaltıda yedim. = stronger focus on an orange
• Yedim kahvaltıda bir portakal. = unusual in neutral speech, more marked or poetic

So the given order is standard and natural.

Literally, kahvaltıda means at breakfast or during breakfast.

But in natural English translation, the whole sentence may be rendered as:

• I ate an orange at breakfast
• I ate an orange for breakfast

The Turkish form itself is based on the locative idea at/in breakfast time, not a special for construction. But in English, for breakfast is often the most natural translation.

It is singular here.

• portakal = orange
• portakallar = oranges

Because there is no plural ending -lar / -ler, and because it is preceded by bir, it clearly means an orange / one orange.

The past tense suffix is often taught as -di, but in real Turkish it changes form depending on vowel harmony and consonant changes.

In yedim:

• the tense part is effectively -di
• the person ending is -m

But when attached to this verb stem, the final result is ye-di-m

So yedim is exactly the normal past-tense first-person singular form of yemek.

You will also see similar patterns like:

• geldim = I came
• içtim = I drank
• baktım = I looked

The form changes according to Turkish sound rules, but the function is the same.

Yes, you can.

There is a difference in nuance:

• Kahvaltıda bir portakal yedim. = I ate an orange
• Kahvaltıda portakal yedim. = I ate orange / I ate some orange / I had orange

Without bir, the object can sound more general or less count-focused. With bir, it clearly refers to one/an orange as a single item.

Then Turkish would usually mark the object with the accusative.

For example:

• Kahvaltıda portakalı yedim. = I ate the orange
• Kahvaltıda o portakalı yedim. = I ate that orange
• Kahvaltıda bir portakalı yedim. = I ate that one orange / a particular orange

So the version in your sentence, bir portakal, is indefinite and non-specific, while accusative marking makes the object specific.

A few useful points:

• kahvaltıda is pronounced with the stress usually near the end in natural speech, though Turkish stress can vary by word type
• portakal has clearly pronounced syllables: por-ta-kal
• yedim is pronounced roughly ye-dim, with ye like yeh

Also remember that Turkish spelling is very regular: words are usually pronounced much more closely to the way they are written than in English. That makes sentences like this easier to read aloud once you know the sound system.