Я несколько раз перечитал это правило.

It means several times or a few times.

Literally:

• несколько = several / a few
• раз = times

So несколько раз is a very common fixed expression for saying that something happened more than once.

The prefix пере- here gives the idea of reading again / rereading.

So:

• читать = to read
• прочитать = to read through, to finish reading
• перечитать = to read again, reread

In this sentence, перечитал shows that the speaker went back to the rule and read it again, in fact several times.

This is a very common learner question.

Russian perfective does not always mean one time only. It means the action is viewed as complete.

Here, несколько раз перечитал means the speaker completed the act of rereading multiple times. You can think of it as several completed rereadings.

Why not imperfective?

• Я несколько раз перечитал это правило = I reread it several times, focusing on completed results.
• Я несколько раз перечитывал это правило = I was rereading / used to reread this rule several times, with more focus on the repeated process or background.

So the perfective is natural here because the sentence presents the repeated action as a finished fact.

In the past tense, Russian verbs agree in gender and number.

So with я:

• a male speaker says я перечитал
• a female speaker says я перечитала

The pronoun я itself does not show gender, but the past-tense verb does.

Because это правило is the direct object, so it is in the accusative case.

But правило is:

• neuter
• inanimate

For neuter inanimate nouns, the accusative looks exactly like the nominative.

So:

• nominative: это правило
• accusative: это правило

That is why nothing changes here.

Compare with a feminine noun:

• эта книга → я перечитал эту книгу

There you can see the accusative ending more clearly.

Because after несколько, the noun normally goes in the genitive plural.

The word раз is a little tricky because its genitive plural is also раз.

So:

• nominative singular: раз
• genitive plural: раз

That is why несколько раз is correct.

This same pattern appears in other expressions of frequency:

• много раз = many times
• пять раз = five times

Yes, sometimes.

Russian often omits subject pronouns when the meaning is clear from context. So in conversation, you might hear:

• Несколько раз перечитал это правило.

However, in the past tense, the verb shows gender and number, but not clearly person by itself, so whether я can be omitted depends a lot on context.

As an isolated sentence, keeping я is clearer and more neutral.

No, Russian word order is fairly flexible.

The version you have is natural and neutral:

• Я несколько раз перечитал это правило.

But other orders are also possible, with different emphasis:

• Я перечитал это правило несколько раз.
  Very natural too; this puts несколько раз later.
• Это правило я несколько раз перечитал.
  This emphasizes это правило.
• Несколько раз я перечитал это правило.
  This emphasizes the repetition.

So the basic meaning stays the same, but the focus can shift.

A helpful stressed version is:

Я нЕсколько раз перечитАл Это прАвило.

Word stress:

• нЕсколько
• перечитАл
• Э́то
• прАвило

For an English speaker, the most important thing is to keep the stress in the right place, especially in перечитАл and прАвило.

Usually, перечитал is better if you mean reread.

Compare:

• прочитал = read through / finished reading
• перечитал = reread

So:

• Я прочитал это правило несколько раз can be understood, but it sounds more like I read this rule several times.
• Я несколько раз перечитал это правило more clearly suggests going back and reading it again and again.

If the intended meaning is specifically reread, then перечитал is the most precise choice.