Student or Learner
1. He is my cousin. (The son of my father's brother)
2. He is my father's brother's son. (The son of my father's brother)
3. She is my cousin. (The daughter of my father's brother)
4. She is my father's brother's daughter.
Are 2 and 4 correct? I mean can we use possessive ['s] two times? (father's brother's)
Are they ok?
And because some languages seem to have different words for different relationships, your cousin is:
Your father's brother's son/daughter
Your mother's brother's son/daughter
Your father's sister's son/daughter
Your mother's sister's son/daughter.
And their parents are your "aunt" and "uncle" whether they are older or younger than your parent, whether they are you mother's relative or your father's, etc.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
Technically, you can use as many possessives as necessary. "My brother's girlfriend's dog's collar is broken", "My brother's girlfriend's dog's collar's buckle is broken". Practically, I think three would be the limit of most people's tolerance.