Hello Muriel,
1) "Ms.Kate, a friend of her mother's...." (what is the meaning of her mother's here. Shouldn't it be "a friend of her mother or her mother's friend" ?)
This "double genative" is commonly used with people, and particularly in the construction in your example. "her mother's friend" is also fine.
2) What's the meaning of 'ever since' ? E.g.: Ever since he was in the army, he has studied hard;
From the time that... Dating back to the time when...
3) "He lives at 341 Bourboun street apartment 23" (in addresses must the word street be translated from a foreign language into English ? E.g.: In Spain street is 'calle'. In this case when I have to say my address in English do I translate the word 'calle' or not ? E.g.:
4) I live at 201 Cervantes calle apartment 101 (or) I live at 201 Cervantes street apartment 101 ? ;
Street should be capitalized -- it's the proper name of the street. I would leave it exactly as is. If someone lived at 221 Rue Charlemagne, I would not write it as "Charlemagne Street." As with any proper nouns, leave them as is, unless the entire phrase has its one translation, e.g., The United States = Les Etats Unis. Leave Street (capital S) as Street and calle as calle.
5) What do we call a organized group of soccer fans that goes to a stadium to watch a soccer/football match ? Is it called organized claque or organized supporters ?
I'm not familiar with this. Organized supporters sounds okay. For a rock band, they are called groupies, but I don't know what soccer fans are called.
6) People who stay outside a stadium trying to sell tickets at a higher price than at a ticket office, are they called street peddler of tickets ?
Scalpers. I don't have a ticket. That's okay - as long as you're willing to pay, I'm sure you'll find a scalper who can sell you one.
7) A special service in which the employees' service is to listen (by phone) to citizens general complaints, for instance, about the bad services offered at a stadium, is it called Ombusdman office ?
Ombudsman is indeed the name for such a service, but it's more commonly found (in my experience) in an organization paid for/supported by the patrons/clients, and not in private industry. The government student loan program has an ombudsman; your local bank has customer service. Also, a company can have an ombudsman to hear issues about ethics, etc., from employees. Still, a company can have an ombudsman for the general public if desired.