Part 3; please read parts 1 and 2 first.

My extended family is quite big but the funny thinks thing is that we all live in different countries.

Again, the countries are different then there has to be more than one of them. You therefore use the plural "countries".

Some relatives live in Canada and sometimes they come to visit us. Others lives live in Australia, another in Spain.

"Others" is like "loro". I live, he lives, she lives, we live, they live.

My family is this an international group of people who are really important to me although even though we live distant far apart.

Part 2: Please read part 1 first

My eldest sister Licia of who is twenty eight years old, got married two years ago and now she's also the mother of my beautiful nephew Tommaso, and finally my middle sister Giulia, of who is twenty years old, that who studies at Perugia.

1/ Italian expresses dates very differently from English. Italian uses "avere", English uses the equivalent of "essere" or "stare".

Italian: Mia sorella ha 28 anni. English: My sister is 28 years old. In English you are not "of" an age, you are an age.

You would never use "that and "who" together like that, but in this case you don't need either. You are simply saying that Giulia studies at Perugia. You might use "who" if you are being clear about which of the sisters is doing what. For example if someone asked if Licia is studying. "Licia? No, she's the one who is married. Giulia is the one who is studying."

We are a really unified close family and we think of ourselves as best friends.

"Unified" and "close essentially mean the same thing here. The repetition of a word like that is called "tautology" in English.

I'm really close to my family especially with my two sisters. We the Most of the time we laugh or argue, but we really take care of each other, because we know that for all types of problem we can talk to each other.

1/ You never say "the most of the time"; it is just "most of the time".

2/ "All" means more than one. Therefore "types" has to be plural.

3/ You have to talk to or talk with someone.

MY FAMILY

It is always composed of, not composed by. "Composed by" would be used if you were talking about a musician who wrote some music. "Consists of" would be another choice of words here.

Both of my sisters are older then me, so, I'm the youngest.

You are indeed, but saying that is redundant since you have already stated that both of your sisters are older. It's not wrong, but it's not needed. Also the comma would come before "so", not after it. "So I'm the youngest" is a complete clause.

My mother and my father Francesca and Remo work together as insurance specialists. like expert of as insurance .

1/ It would be more common to say "My mother Francesca and my father Remo" to keep all of the information about each person together.

2/ There is no real equivalent to the use of "come" in English; people's jobs are described differently. You would say "I am an insurance specialist", "he is a fireman", "she is a doctor", etc. You would not use "like", which would be a literal translation of the Italian "come".

3/ "Insurance expert" would not be a common usage. I'm not sure what an expert in insurance would do. Some people do specialise in the field of insurance, though; they may calculate risk tables 9though they are called "actuaries", others may consult on the best insurance to get. I would therefore just use the more generic "specialist".

4/ You can be an expert in something or at something , but you would not be an expert "of" something, and certainly not "as of" something.

To be continued...