Я позвонил кузену вчера.

Because позвонить takes the person you call in the dative case, not the nominative.

So:

• кузен = cousin (dictionary form, nominative)
• кузену = to the cousin / to my cousin (dative)

This is very common with звонить / позвонить:

• позвонить другу
• позвонить маме
• позвонить врачу

English says call someone, but Russian grammar here is closer to call to someone in structure, even though there is no preposition.

This is an aspect question.

• позвонил = perfective
• звонил = imperfective

In this sentence, позвонил presents the call as one completed action: the speaker made the call yesterday.

By contrast, звонил could mean something more like:

• was calling
• called with focus on the process or fact, not completion
• possibly called repeatedly or in a less bounded way, depending on context

So Я позвонил кузену вчера most naturally means a completed, one-time call.

It shows that the verb is in the past tense, and specifically masculine singular.

Russian past tense agrees with gender and number:

• я позвонил = I called (male speaker)
• я позвонила = I called (female speaker)
• мы позвонили = we called
• они позвонили = they called

So this sentence suggests the speaker is male.

It would be:

Я позвонила кузену вчера.

Only the past-tense verb changes:

• позвонил = male speaker
• позвонила = female speaker

Everything else stays the same.

Yes, often it can.

Russian frequently drops subject pronouns when the subject is clear from context. So in conversation, you might hear:

Позвонил кузену вчера.

However, without context, that can sound less self-contained than the full sentence. Including Я makes it explicit and is very normal.

So:

• Я позвонил кузену вчера = full and clear
• Позвонил кузену вчера = natural in context, especially in speech

Yes, Russian word order is flexible.

All of these are possible:

• Я позвонил кузену вчера.
• Я вчера позвонил кузену.
• Вчера я позвонил кузену.

They all mean basically the same thing, but the emphasis changes.

Very roughly:

• Я вчера позвонил кузену = neutral, common way to mention yesterday
• Вчера я позвонил кузену = stronger focus on yesterday
• Я позвонил кузену вчера = also correct; вчера can sound a bit like added time information or a point of focus at the end

So the sentence is grammatical, but Russian uses word order partly for information structure, not just grammar.

It is a real and correct word, but many Russians more commonly say:

• двоюродный брат = male cousin
• двоюродная сестра = female cousin

So кузен is understandable, but it can sound a little less everyday in some contexts. It is still perfectly grammatical.

Yes.

Кузен is masculine, so кузену means to a male cousin.

For a female cousin, you would use:

• кузине = to a female cousin

Though again, many speakers would more often use:

• двоюродной сестре = to a female cousin

Russian often leaves out possessive words like my when the meaning is obvious from context.

So Я позвонил кузену вчера can naturally mean:

• I called my cousin yesterday

Even though my is not stated.

If you want to make it explicit, you can say:

Я позвонил моему кузену вчера.

That is also correct, but not always necessary.

Russian has no articles like a or the, so nouns do not automatically show that distinction.

So кузену could mean, depending on context:

• to a cousin
• to the cousin
• to my cousin

The exact meaning comes from context, not from an article.

That is very normal in Russian.

The stress is important:

• Я — ya
• позвонил — stress on the last syllable: пазванИл
• кузену — stress on зе: кузЕну
• вчера — stress on the last syllable: вчерА

A useful detail: in unstressed position, Russian о often sounds more like a, so позвонил is pronounced closer to пазванил than a careful po-zvo-nil.

Not always, but in this sentence, yes.

With a person in the dative, позвонить usually means to phone / call:

• позвонить кузену = call your cousin

But the verb is related to ringing in general, so in other contexts it can also be used for things like:

• позвонить в дверь = ring the doorbell

So the surrounding grammar helps show the meaning. Here, with кузену, it clearly means a phone call.