Она говорила с гневом.

Because the subject is она (she), and Russian past tense agrees with gender and number.

• говорил = masculine singular
• говорила = feminine singular
• говорило = neuter singular
• говорили = plural

So Она говорила means she was speaking / she spoke.

Говорила is:

• past tense
• imperfective aspect

The base verb is говорить (to speak, to talk), which is imperfective.

Here the imperfective suggests the speech is viewed as a process or manner of speaking, not as one completed result. In other words, the sentence focuses on how she was speaking, not on one finished statement.

Compare:

• Она говорила с гневом. = She was speaking with anger / She spoke angrily.
• Она сказала это с гневом. = She said it with anger.
  This sounds more like one completed utterance.

Гневом is in the instrumental case.

After с meaning with, Russian normally uses the instrumental:

• с другом = with a friend
• с интересом = with interest
• с гневом = with anger

The noun is гнев. In the instrumental singular, it becomes гневом.

So:

• nominative: гнев
• instrumental: гневом

No. С can take different cases depending on meaning.

In this sentence, с means with, so it takes the instrumental:

• с гневом = with anger

But с can also mean from/off, and then it often takes the genitive:

• с полки = from the shelf
• с работы = from work

So the meaning of с tells you which case is being used.

Yes, it is natural, but it sounds a bit more literary or elevated than some everyday alternatives.

It means something like:

• with anger
• in an angry manner
• angrily

Common alternatives include:

• сердито = angrily, crossly
• гневно = angrily, wrathfully
• со злостью = with malice / angrily / with spite

So с гневом is correct and expressive, but in casual speech Russians might often choose an adverb instead.

You can. Those are valid alternatives.

The difference is mostly stylistic:

• говорила с гневом = literally spoke with anger; a noun phrase, slightly more descriptive or literary
• говорила гневно = spoke angrily; concise, adverbial
• говорила сердито = spoke angrily / irritably; often a bit more everyday

So the sentence with с гневом is not more grammatical than the others; it just expresses the idea in a different style.

Often yes.

Russian frequently drops subject pronouns when the subject is clear from context. So if everyone already knows who is being talked about, you could simply say:

• Говорила с гневом.

However, keeping она can help by:

• making the subject explicit
• adding contrast or emphasis
• sounding clearer out of context

So она is not always required, but it is perfectly normal here.

Yes. Russian word order is flexible.

All of these are possible:

• Она говорила с гневом.
• С гневом она говорила.
• Она с гневом говорила.

The basic meaning stays the same, but the emphasis changes:

• Она говорила с гневом. = neutral
• С гневом она говорила. = emphasizes with anger
• Она с гневом говорила. = also highlights the manner somewhat

English word order is more fixed, but Russian uses word order more for emphasis and information structure.

They are close, but not identical.

• с гневом = with anger, describing the manner of the speech
• в гневе = in anger / in a rage, describing her state

So:

• Она говорила с гневом. = Her speech had an angry tone.
• Она говорила в гневе. = She was speaking while in a state of anger.

In many contexts they overlap, but с гневом focuses more on how she spoke, while в гневе focuses more on the emotional state she was in.

The stress is:

• она́
• говори́ла
• с
• гне́вом

So: она́ говори́ла с гне́вом

A rough pronunciation guide:

• она́ = a-NA
• говори́ла = ga-va-REE-la
• гне́вом = GNYE-vam

A useful thing to notice is that unstressed о often sounds closer to a in actual pronunciation, which is why говорила sounds roughly like gavaríla.

No. Russian does not have articles.

So Она говорила с гневом does not contain words corresponding to with the anger or with an anger. Russian simply says with anger, and context supplies the rest.

This is very normal in Russian and something English speakers have to get used to.