Learn Farsi: هر یک از سینی‌ها سی کاپ‌کیک دارد. - Each one of the trays has thirty cupcakes.

The true subject of the sentence is the distributive pronoun هر یک (each one), which is singular. Just like in English where we say "each one has" (not "have"), Farsi uses the third-person singular verb دارد when a subject phrase begins with هر یک از or هر کدام از.

Could I use هر کدام از instead of هر یک از here?

Yes, they are completely interchangeable in this context and both mean "each one of." هر کدام از is slightly more common in everyday spoken Farsi, whereas هر یک از can sound just a tiny bit more formal, though both are perfectly natural.

Why is کاپ‌کیک (cupcake) in the singular form when the sentence specifies thirty (سی) of them?

This is a crucial rule to remember: in Farsi, any noun that directly follows a number must always remain singular. Even though the English translation uses the plural "cupcakes," Farsi requires the singular کاپ‌کیک after the number سی.

What is the function of the invisible break in the middle of کاپ‌کیک?

That is a "half-space" (zero-width non-joiner), commonly used in Farsi for compound words. Because "cupcake" is a borrowed compound, the half-space links کاپ and کیک into one vocabulary item without letting their letters connect physically, making it much easier to read.