Part 2, please read part 1 first.

I'm attending lessons with them, I'm listening to them and I'm trying to deal with my shyness to speak with them in the best way I can.
They are so patient and they are so similar to us, spending time with them it's is a real pleasure.,

1/ This is the same issue. You have already said what it is that is a real pleasure, so you don't need "it". 2/ I recommend stopping the sentence at that point so that it does not become hard to read.

over this Furthermore it's awesome noticing how it's so helpful to improve my English skills deal by dealing with the "problem" directly: it's the evidence that if you need to communicate, you are even more stimulated to learn a language different from your native one.

1/ I'm not sure but I think that "over this" may have come from the word "oltre", but it isn't really used that way in English. I suggest "furthermore".

2/ Noticing is OK, but I would suggest "to see". It's really more about revealing and observing something (seeing it) rather than just having your attention drawn to it (noticing). However I would not call it a mistake.

3/ There is no way that I can explain the grammar behind "deal" vs "by dealing" in the space available; just trust me on that one.

4/ It's evidence, but it's not the one and only piece of evidence. I would therefore drop the "the" here.

So...good luck for all the mistakes that I've done in this text

I'm not sure what you're trying to say with the expression "good luck" there.

Yes, there appear to have been a lot of corrections but that's only because I've tried to explain them, not just give them. Overall there are only a few issues with this, and your writing is of a very good standard.

Part 1

Living an awesome experience

You have not joined to a site, you always join a site. "Joined to" is normally used in a physical sense (the camera is joined to the tripod) or for a metaphor for something similar ("It is like they were joined to each other at the hip".) However with a site, club or association, you simply "joined" it. Remember that English is always capitalised.

Even if I feel my written and conversational English skills are not so high, luckily I've been selected...so my desire to improve is has grown.

1/ Conversation is a noun, conversational is an adjective. 2/ It's not completely wrong but it would be uncommon to say "not so high"; "not very high" or "not very advanced" would be more common. Though I disagree about your written skills; they are far better than average. 3/ You would not say that something "is grown" (though you might say "is fully grown") but in this case you are talking about an event in the past (your selection) which caused your desire to grow; it would be better to use the past form "has grown" or, if you want to stay in the present, "is growing".

Next year I'm probably going to the US and will stay there for a month and a half, but it's all to define be finalised yet.

1/ There are very few country names which use the definite article in English but "The" United States" is one of them. 2/ You are talking about something in the future; while English does sometimes use the present form for a future event (the same as Italian) in this type of construction it sounds more natural to use the future tense (will). 3/ You could get away with not using "for" but again it sounds more natural (or certainly more well spoken) to use it. 4/ Plans can be defined (though you would not use the infinitive ("to define") here. You are missing the verb that corresponds to "essere"; you would say "it is to be defined". However I would probably use "finalised" instead since there is some uncertainty about whether it will happen.

What it's is awesome and exciting now it's is the direct experience that I'm having with American guys and girls here in Italy.

"It" (as part of "it is" or "It's") is most commonly a pronoun, but in this case you are already using words (like "what") that make the "it" pronoun redundant. What is exciting is...  the direct experience. You would use "It" if you didn't have a word like "what"; "It is (or "it's") exciting to have the direct experience..." etc.

Living an awesome experience.