Перелистывай страницы учебника аккуратнее, пожалуйста.

Because перелистывай is the imperfective imperative (from перелистывать). It typically means:

• do it repeatedly / as a general instruction: “(Whenever you do it,) turn the pages more carefully.”
• keep doing it in a careful way (ongoing behavior)

Перелистай would be the perfective imperative (from перелистать) and would more likely mean:

• do it once / finish one action: “Turn (through) the pages (once),” often implying completion.

So the imperfective fits a “habit/instruction” tone.

The prefix пере- often suggests moving across / from one to another. In page-turning verbs, перелистывать commonly means:

• to flip through pages (turning from page to page, often quickly or repeatedly)

Compare:

• листать = to leaf through, flip through (general)
• перелистывать = to flip/turn over pages one after another (very natural for page-turning)

In this sentence, перелистывай страницы is basically “flip/turn the pages.”

Yes—перелистывай is the singular informal “you” command (to a friend, child, family member, etc.).

Polite / formal or plural form:

• Перелистывайте страницы учебника аккуратнее, пожалуйста.

So the switch is:

• -й (informal singular) → -йте (polite singular OR plural)

страницы is accusative plural (the direct object: “pages”). учебника is genitive singular meaning “of the textbook”.

Russian commonly uses Noun + Genitive to express possession/material:

• страницы учебника = “the textbook’s pages” / “pages of the textbook”

The dictionary form is учебник (nom. sg.), but after страницы you need genitive: учебника.

Yes, Russian can say that too, but the meaning shifts slightly:

• Перелистывай учебник аккуратнее.
  = “Flip through the textbook more carefully.” (the object is the book as a whole)

• Перелистывай страницы учебника аккуратнее.
  = “Turn the pages of the textbook more carefully.” (focuses on the pages themselves)

Both are natural; the original is just more explicit.

аккуратнее is the comparative form of the adverb аккуратно (“carefully/neatly”):

• аккуратно → аккуратнее = “more carefully / more neatly”

Russian very often prefers the single-word comparative (аккуратнее) over более + adverb (более аккуратно).
Более аккуратно is possible, but it sounds more formal/bookish.

Also, the comparative here implies: more carefully than you are doing now.

Common stresses (most neutral pronunciation):

• перелИстывай
• страни́цы
• уче́бника
• аккура́тнее
• пожа́луйста

Stress matters a lot in Russian, and these are the standard patterns.

Because пожалуйста here functions as a parenthetical politeness marker (like “please”), and it’s commonly separated by commas in Russian punctuation.

Both are seen, but these are typical:

• ..., пожалуйста. (very common)
• Пожалуйста, ... (when “please” is at the start)

In casual writing, commas may be omitted sometimes, but the comma is the standard choice.

Yes, word order is flexible, but it changes emphasis.

Very natural options:

• Перелистывай страницы учебника аккуратнее, пожалуйста. (neutral)
• Перелистывай страницы учебника, пожалуйста, аккуратнее. (puts “please” in the middle)
• Аккуратнее перелистывай страницы учебника, пожалуйста. (emphasizes “more carefully”)

The original sounds like a straightforward instruction with a polite softener at the end.

Yes, a few common choices:

• перелистывать = flip/turn through pages (very common for books)
• листать = leaf through / flip through (often suggests browsing)
• переворачивать страницу = turn a page over (more literal; often one page)
• открывать/раскрывать = open (not “turn pages,” but sometimes learners confuse these)

Your sentence is idiomatic because перелистывать страницы is a typical collocation.