Ben kahvaltıda kaşarlı tost yiyorum.

Yes, Turkish often drops subject pronouns because the verb ending already shows the person.

Here, yiyorum already means I am eating, so ben is not strictly necessary. The sentence could simply be:

Kahvaltıda kaşarlı tost yiyorum.

Using ben can add:

• emphasis: I am eating...
• contrast: I am eating cheese toast, maybe someone else is eating something different
• a slightly clearer beginner-style sentence

So ben is correct, but often optional.

Kahvaltı means breakfast.

The ending -da / -de / -ta / -te is the locative suffix, usually meaning in, on, at.

So:

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

In this sentence, it is naturally understood as for breakfast or at breakfast time.

This is just a natural Turkish way to express meals and meal times.

Turkish often uses the locative with meal words:

• kahvaltıda = at breakfast
• öğle yemeğinde = at lunch
• akşam yemeğinde = at dinner

So even if English says for breakfast, Turkish may prefer a structure closer to at breakfast.

Kaşarlı means with kaşar cheese or more naturally cheese-filled / cheesy, depending on context.

It comes from:

• kaşar = a type of cheese very common in Turkey
• -lı / -li / -lu / -lü = a suffix meaning with or having

So:

• kaşarlı tost = toast with kaşar cheese
• more naturally in English: a cheese toastie or a grilled cheese sandwich, depending on context

In Turkish, adjectives usually come before the noun, just like in English.

So:

• kaşarlı tost = cheese toast
• büyük ev = big house
• sıcak çay = hot tea

Here, kaşarlı describes what kind of tost it is.

Turkish does not use articles the same way English does.

English often needs:

• a cheese toast
• the cheese toast

Turkish often leaves this unmarked:

• kaşarlı tost

If you say bir kaşarlı tost, it means a/one cheese toast and can sound a little more specific or countable.

Without bir, the sentence sounds very natural and simply refers to the food being eaten.

This is about the accusative case.

In Turkish, a direct object usually takes the accusative ending -(y)ı / -(y)i / -(y)u / -(y)ü when it is specific/definite.

So:

• kaşarlı tost yiyorum = I am eating cheese toast / a cheese toast (non-specific)
• kaşarlı tostu yiyorum = I am eating the cheese toast (a specific one)

Because the sentence is talking about the food in a general, indefinite way, tost stays unmarked.

The dictionary form is yemek = to eat.

In this sentence:

• verb stem: ye-
• present continuous suffix: -iyor
• 1st person singular ending: -um

This gives yiyorum = I am eating.

A useful thing to notice: with some verbs, the form changes a little when -iyor is added. So learners memorize:

• yemek → yiyorum
• demek → diyorum

So yiyorum is the normal present continuous form of yemek.

Most directly, yiyorum means I am eating.

However, Turkish -iyor can sometimes also be used for a present-time habit, depending on context. So this sentence could mean:

• I am eating cheese toast for breakfast right now
• or, in some contexts, I eat cheese toast for breakfast

If you want a more habitual or general meaning, Turkish can also use the aorist:

• Ben kahvaltıda kaşarlı tost yerim. = I eat cheese toast for breakfast.

So yiyorum usually feels more immediate or current.

No, Turkish word order is flexible, although the most neutral order is often:

Subject + time/place + object + verb

That is exactly what you have here:

• Ben = subject
• kahvaltıda = time/context
• kaşarlı tost = object
• yiyorum = verb

You could move parts around for emphasis, for example:

• Kahvaltıda kaşarlı tost yiyorum.
• Kaşarlı tost yiyorum ben.

But the version you were given is a very natural, standard order for learners.

Two letters here are especially important:

• ş = sh sound, like in shoe
• ı = a vowel that does not exist in standard English; it is a dull, central vowel, somewhat like the vowel in the second syllable of sofa, but said further back and without rounding the lips

So:

• kaşarlı sounds roughly like kash-ar-luh
• kahvaltıda sounds roughly like kah-vahl-tuh-duh

These are only rough guides, but they help beginners avoid reading:

• ş as plain s
• ı as English ee or eye, which would be incorrect