Мне нравится тот отрывок, где главная героиня записывает свою догадку в дневник.

Нравиться works differently from English to like. It literally means something like to be pleasing.

So in Мне нравится тот отрывок:

• мне = to me (dative case)
• нравится = is pleasing
• тот отрывок = the thing that is pleasing

So the structure is closer to That excerpt is pleasing to me than to I like that excerpt.

You could say Я люблю этот/тот отрывок, but любить usually sounds stronger, more emotional, or more permanent. Мне нравится is very natural for talking about a scene, passage, song, film moment, and so on.

Because отрывок is the grammatical subject of нравится.

With нравиться, the thing that is liked stays in the nominative:

• Мне нравится отрывок
• Мне нравится книга
• Мне нравятся книги

Notice that when the thing changes number, the verb changes too:

• нравится for singular
• нравятся for plural

So here тот отрывок is nominative singular, and that is why the verb is нравится.

Тот means that and points to a specific excerpt.

So тот отрывок = that excerpt / that passage.

It often implies one of these ideas:

• the speaker has a particular excerpt in mind
• the excerpt was mentioned before
• the speaker is mentally pointing to a specific part of the text

If you said just Мне нравится отрывок, где..., that can also be grammatical, but тот makes it more specific.

Also, тот agrees with отрывок:

• masculine
• singular
• nominative

Because где главная героиня записывает свою догадку в дневник is a subordinate clause describing отрывок.

Russian normally separates this kind of descriptive clause with a comma:

• тот отрывок, где...
• дом, где я вырос
• книга, которую я читаю

So the comma is required here.

This is very common in Russian.

Где literally means where, but it can also be used with things like:

• сцена = scene
• момент = moment
• часть = part
• отрывок = excerpt/passage

So отрывок, где... means something like:

• the passage where...
• the excerpt in which...

Russian treats this very naturally.

A more formal or more literal alternative would be отрывок, в котором..., but где is completely normal and often sounds more natural in everyday speech.

Russian often uses the present tense when talking about the contents of books, films, stories, and scenes. English does this too:

• I like the part where she writes it in her diary.
• In this chapter, the hero discovers the truth.

So записывает does not necessarily mean the action is happening right now in real life. It is the normal tense for describing what happens in a text or narrative.

Because записывает is imperfective, and that fits this context well.

Here the speaker is describing what happens in the excerpt, not emphasizing the result as a one-time completed event. Imperfective is often used:

• to describe scenes
• to summarize plot
• to present an action as part of the unfolding passage

If you used запишет, that would be future perfective and would usually mean will write down, which does not fit here.

If you were retelling the story as a completed past event, you might say записала, but in plot summary Russian commonly uses the present: записывает.

Because the guess belongs to the subject of the clause: главная героиня.

Russian usually uses свой when the possessor is the same as the subject:

• Она записывает свою догадку = She writes down her own guess

If you said её догадку, it could sound like the guess belongs to some other female person, not necessarily the heroine herself.

Also, свою agrees with догадку, not with the owner:

• догадка is feminine
• accusative singular of своя is свою

So свою догадку is exactly the form you expect.

Because it is the direct object of записывает.

She writes down what?
свою догадку

The basic noun is догадка. In the accusative singular, it becomes догадку.

This is a standard feminine pattern:

• книга → книгу
• идея → идею
• догадка → догадку

Because Russian uses:

• в + accusative for direction or movement into something
• в + prepositional for location inside something

Here записывать в дневник is understood as putting the information into the diary, so Russian uses в дневник.

Compare:

• Она записывает мысль в дневник = She writes the thought into her diary
• Это написано в дневнике = This is written in the diary

So:

• в дневник = into the diary
• в дневнике = in the diary

No, Russian word order is flexible, although the original sentence is the most neutral and natural version.

The given order:

Мне нравится тот отрывок, где главная героиня записывает свою догадку в дневник.

sounds smooth and neutral.

You could also move things around for emphasis, for example:

• Тот отрывок, где главная героиня записывает свою догадку в дневник, мне нравится.
• Главная героиня записывает свою догадку в дневник в том отрывке, который мне нравится.

But these versions change the focus or sound more marked. For a learner, the original sentence is a very good default model.