Я позвонил матери.

Because позвонить takes the dative case for the person you call.

• мать = nominative dictionary form
• матери = dative singular

So:

• Я позвонил матери = I called my mother
• literally, something like I placed a call to mother

This is a very common Russian pattern: the person receiving something, being spoken to, written to, or called is often in the dative.

This is a question of aspect.

• позвонить = perfective
• звонить = imperfective

In this sentence, позвонил usually means a completed single action:
I called / I made a call.

By contrast:

• Я звонил матери often means I was calling mother, I called mother (at some point / habitually / without focusing on completion), or I tried calling mother, depending on context.
• Я позвонил матери clearly presents the call as one completed event.

So if the meaning is a single finished call, позвонил is the normal choice.

It marks the past tense and also shows masculine singular.

Russian past tense forms agree with the subject in gender and number:

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

So Я позвонил матери tells you that the speaker is male.

Only the verb form:

• Я позвонила матери.

Everything else stays the same.

That is because in the Russian past tense, the verb agrees with the speaker’s gender when the subject is я.

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

So:

• Я позвонил матери naturally means I called my mother
• adding моей is possible, but often unnecessary:
  • Я позвонил моей матери

The version without моей can sound more natural and less heavy when it is already clear whose mother is meant.

Both can mean to mother / to my mother, but the style is different.

• матери comes from мать and sounds more formal, neutral, literary, or serious
• маме comes from мама and sounds more everyday, warm, and conversational

Compare:

• Я позвонил матери. = a bit more formal or narrative
• Я позвонил маме. = very natural in daily speech

In conversation, many people would more often say маме.

Yes, it can often be omitted.

Russian frequently drops subject pronouns when the subject is clear from the verb form or context.

So both are possible:

• Я позвонил матери.
• Позвонил матери.

The version with Я is more explicit and may add contrast, emphasis, or simply sound more complete out of context.

Yes. Russian word order is flexible.

All of these are possible, with different emphasis:

• Я позвонил матери. = neutral
• Матери я позвонил. = emphasizes mother
• Позвонил я матери. = can emphasize I
• Я матери позвонил. = also possible, slightly different rhythm/focus

The basic meaning stays the same, but the information focus changes.

Yes. The standard Russian pattern is:

• позвонить + dative
• звонить + dative

Examples:

• позвонить другу = to call a friend
• звонить сестре = to call a sister
• позвонить врачу = to call the doctor

So матери is not unusual at all; it is exactly what the verb requires.

The dictionary form is позвонить.

When you look up Russian verbs, you normally find them in the infinitive:

• позвонить = to call, to phone

From that, you get:

• позвонил = called (masculine past)
• позвонила = called (feminine past)
• позвоню = I will call
• позвони = call! / give a call!

Here it is dative singular.

For мать, the singular forms are somewhat irregular, so they are worth memorizing:

• nominative: мать
• genitive: матери
• dative: матери
• accusative: мать
• instrumental: матерью
• prepositional: матери

So матери can represent more than one case in different contexts. In this sentence, we know it is dative because позвонить requires the dative.

The stress is on the first syllable:

• мАтери

A rough guide for English speakers:

• Я ≈ ya
• позвонил ≈ pazvaNEEL
• матери ≈ MAteri

So the whole sentence is approximately:

• ya pazvaNEEL MAteri

The exact vowel quality is different from English, but this is a useful starting point.

In theory, yes, because Russian does not use articles like a or the.

But in normal context, Я позвонил матери will usually be understood as I called my mother unless the situation clearly points to some other mother.

Russian relies heavily on context, much more than English does in this kind of sentence.