There were my cousins, my uncle, my aunt, my grand parents and of course my parents.

The use of "my" every time is redundant. The reason I left the last "my" in the sentence, is that when saying (speaking out loud) a list of items, it is natural to pause a little before saying the last item in the list. The inclusion of "my" at the end also indicates to the listener that this is the end of a list, and it sounds nice to my ears. (This is only true with a longer list like you have > 3 items).

I don't often go to the library but I think it's a really warmonderful place.

Either you meant "wonderful" or "warm".

You can smell the books's smells, etc.

when making plural words that end in "s" their possessive form, you put the apostrophe (') at the end of the plural form. e.g.
friend -> friends -> friends' ("All of my friends' toys were brought to my house")

However, a more natural sounding sentence would just be "You can smell the books and such."

I knew it fromby name because it's a really famous movie, but I've never watched the movie it nor read the book.

The phrase "knew it by name" is extremely common in English.

My cousin told me that the film is really good and the universe is similar as the Hunger Games's one.

They are both dystopican.

"dystopic" isn't really used much in English. "Dystopian" is much more frequently so.

So I thought it was a great idea to read the book and then, watch the movie.

I started reading the book 4 days ago, and at the moment, I appreciate it.

There are's not a lot of action at the moment, but ithat's normal because I am only at the page 30.

Another common phrase similar to "but that's normal..." is "but that's to be expected..."

If I do that, then I will finish the book in roughly 1 month, and I will can read the two other two books later (the suite?).

I'm not sure what you mean by "the suite", possibly "the sequels"?
Also, the word order "the other two" is much much more common than "the two other".

I am currently at the third chapter.

It's pretty common for native English speakers to say "on the third chapter", but, grammatically speaking, they're wrong and you're correct. Just an FYI (for your information), as you'll likely come across this in the wild/real world.

It's a test which/that allows you to know which faction you belong in.

"which" and "that" in this context can be swapped out with each other.

There are 5 different factions which/that represent a characteristic of their personality.

For example, there are Abnegation, and Candor, or amongst others.

Since "Dauntless", "Amity", "Erudite", and "Factionless" are not explicitly called "other", it does not make sense to use your original sentence. "amongst others", is a way to say that your list is incomplete.

I don't remember all the faction's names.

The plurality of "names" takes care of the plurality of "faction". You could also use "factions' names" instead, but that would be a less common way to say it.

But the point is that when she did the test, itshe passed somethingin a weird way.

I'm not 100% sure what you were trying to say with "it passed something weird".

Her different characteristics can't show clearly whatouldn't clearly show what/which faction she belonged in/to.

It's something really dangerous for her and she haves to tell it to nobody.

Since being "Divergent" is dangerous by itself (and not ONLY for Beatrice) you wouldn't include "for her" (therefore making it apply generally to any "Divergent").

Also, the phrase "she has to tell it to nobody" sounds weird, a more natural sounding sentence would be "she can't tell anyone/anybody"

With this result, aton the Ceremony Day, the next/following day, she will have to choose which faction she will integrate into.

She was supposinged to tell it to nobody but when she came home, she told it to her brother Caleb.

"She was supposed to tell it to nobody" also sounds a little weird, a more natural sentence would be "She wasn't supposed to tell anyone/anybody"

In the next chapter, I think we will know/learn which faction she will integrate I thinkinto.

Alternate suggestion:
"In the next chapter, we will learn which faction she will integrate into (I think)." (The parenthesis () turn their contents into an "aside", which basically gives you the ability to interrupt the flow of the sentence in order to add more information)

It'sll be a turning point in the story.

Future tense, since you haven't yet read that part of the story.

Nevertheless, (according to me,) I think it's a possible that she will finally choose thisat one anyway, but I don't know.

In your original sentence, it wasn't super clear to me which faction you were talking about. The suggestions I made make it clearer that you are trying to say "the one Beatrice might choose is the one faction she excluded" (which is "Dauntless" if I recall correctly).

I hope you enjoy/ed reading my text.

both present and past-tense work here. Since technically we haven't yet finished reading all of your post by this point, it could be present-tense, but usually you would used past-tense, as we have already read (almost) everything.

Please tell me how you found my English to be!