Hola Sthefi, here we go:

An Old Fashioned Girl (Book)

Today I started to read "An Old Fashioned Girl", one of my many books I have in English, these books were a gift that a neightbour (vecina) gave to me about more than 5 months ago.

Use "these" instead of "those" if you're talking about something you still have and you're not trying to differentiate between one set of books and another, for example.

"More than 5 months ago" is all you need.  It is already indefinite so you don't need to add the "about".

I know I need to do my best to improve my vocabulary, perhaps (sin embargo) there are so many words that I still will not be able to understand! One of my friends (Who studies English at the University with me) told me that in these gift books, the verbs, grammar and some prepositions are in Old English.

"gift books" ... Just use "books", your audience knows that they were given to you at this point.

Maybe the Spanish speaking world and English speaking worlds could get together and write up a treaty reducing the number of words in each language!

The thing is, I can understand the context (which is so important, at least) but words like "boldly", "beseeching", "lawlessness", "bewilderment", "leisurely" ,"thingamabob", "crinkles"... and so on, these are words that are completly (completamente) new and strange to me!

"newer" and "stranger" would be used if you were saying something like ...  These books are newer and stranger than those books (comparing).  Since you are just talking about how they feel to you just say "new" and "strange".

I find that rereading a passage a number of times each day for a few days fixes the words in my memory, even if I'm learning them shearly by context.

Some of these corrections are just corrections of typos, I'm sure, but I just want to be sure.

The worst thing is I have two English dictionaries, but they don´t have those words. Mmm, maybe I have to buy an Oxford dictionary... 

Just ask one of your partners! That's what is so great about this site.

I had been read a few of pages about in this book, it seems very interesting and great (Mmm, I don´t know how I could translate "Pese a no entenderlo del todo", in English) I´m trying to read it aloud to can practise my english reading too.

Pese a no entenderlo del todo = In spite of not understanding everything

In the morning, like I wrote before, I was reading aloud and then a guy looked at me surprised and he turned his head around away when I felt observed (Observada, sintiendo su mirada) by him.

It was a little funny to me, only I need to have the chance to speak English in my University, outside of there, I don´t have many people to talk it.

Well, a sure sign of insanity is when someone goes around talking to themselves! ;p

My dad knows, but it´s very basic, otherwise we have Internet and we could do almost everything with it.

You're vocabulary is pretty good Sthefi, just remember, even though it seems to grow slowly, you are continually adding new layers of English knowledge and understanding.  <<play some corny music>>

If these corrections are too detailed, just say so.

¡Espero que eso te ayuda!