Learn Farsi: هر کدام از کاپ‌کیک‌ها خامه‌ی وانیل دارد. - Each one of the cupcakes has vanilla cream.

Even though the noun following از is plural, the true grammatical subject of the sentence is the distributive pronoun هر کدام (each one). Just like in English where we say 'Each one... has' (not have), Farsi uses the third-person singular verb دارد because it is referring to the cupcakes individually.

Could I use هر یک از instead of هر کدام از in this sentence?

Yes, absolutely. هر یک از and هر کدام از both mean 'each one of' and are interchangeable here. هر کدام از (each which of) is very common in spoken and everyday Farsi, while هر یک از (each one of) can sound just a little bit more formal or literary.

Why is there an explicit ی added to خامه in the phrase خامه‌ی وانیل?

The word for cream, خامه (khâmeh), ends in a 'silent he' (ه) which produces an 'e' vowel sound. When you link it to وانیل using the Ezafe (the grammatical connector meaning 'of'), you cannot just add another vowel sound. The ی acts as a consonant bridge between the two vowels, making it khâmeh-ye vânil (cream of vanilla).

Does the English loanword کاپ‌کیک (cupcake) always use the standard Farsi plural suffix ها?

Yes. When modern foreign words are borrowed into Farsi, they almost always take the regular Farsi plural suffix ها (-hâ). Unlike some older Arabic loanwords that kept their original broken plurals, modern English loanwords are treated as standard Farsi nouns.