During my childhood, my mother had a lot of books and she gave mepassed on her passion aboutfor them.

"gave me" is fine, but "passed on" is a more natural phrase for this context.
Instead of "about" we would use "for" here.

We had a lot of different books in our toilets, and I spendt a few hours sat oin there onlyjust to read my mother's books.

"spent" is the past tense of "spend". Don't be tricked by "spend" looking like it's in the past tense already!
Since you said the books are "in" the toilets I would assume you're referring to the room - so you'd sit "in" the room. The alternative would be that the books were in the toilet bowl, which wouldn't make for good reading material.
Instead of "only", I'd use "just" here. They mean more or less the same thing, but "just" is more commonly used in this kind of context.

She bought me a lot of comics when I was younger, and my first "real" novel for mywhen I was ten years old.

Alternatively, if it was for your birthday: "for my 10th birthday".

Now, it is old, and dirty, with a lot of damages, because I took it with me every timwhere, but it has two stories: the story wrote insideithin the pages, and the story I engraved onupon it.

"engraved upon it" is somewhat poetic language, but I imagine that's your intent here.
Since the adjectives "old" and "dirty" are not directly preceding a noun they should be joined with "and". The rule about putting a comma between two adjectives is for when they are directly in front of a noun.
"I took it with me every time" leaves me questioning "every time you did what?" - instead I would phrase it as "I took it with me everywhere". "every time" is used when we refer to doing a specific activity.

I know a lot of people don't be agree with that, but I love to damage my books, cornedogear the pages, write inside...

I'm not exactly sure what you meant by "corne", but if you're referring to the act of folding over the corner of a page then we'd refer to that as "dogearing". This is because the folded over part resembles a dog's ear. You can use "dogear" as a verb, like I have in the corrected sentence.

During my childhood, my mother had a lot of books and she gave me her passion aboutfor them.

We had a lot of different books in our toiletbathrooms, and I spend a few hours sat on there only to read my mother's books.

The word “toilet” almost always refers to the actual object you use to go to the bathroom. I hope you did not have books inside your toilet.

She bought me a lot of comics when I was younger, and my first "real" novel for my ten years oldth birthday.

Now, it is old, and dirty with a lot of damages, because I took it with me every time, but it has two stories: the story wrote inside, and the story I engraved on.

In English, if only two things are being listed, they must be joined with “and.”

For example:
Sugar and spice.
Old and dirty.
New and interesting.
Jackets and mittens.

During my childhood, my mother had a lot of books and she gave me her passion aboutfor them.

We had a lot of different books in our toilets, and I spend a fewmany hours sat onitting there only to read my mother's books.

Since you're talking about your past habit of reading on the toilet and not just one event, it's better to say "many". You spent many hours in general, but at one single time you would spend "a few" hours reading .

She bought me a lot of comics when I was younger, and my first "real" novel for mywhen I was ten years old.

Now, it is old, dirty, and with a lot of damages, because I took it with me every timwhere, but it has two stories: the story wroitten inside, and the story I engraved on it.

We say the story "written" because a story can't write, but a person writes a story. Therefore we use passive voice because the story is the object that receives the action of "writing".

I know a lot of people don't be agree with thait, but I love to damage my books, corner the pages, write inside...