Men's soccer has been held in every Summer Olympics, except for the inaugural competition in 1896 and the Los Angeles 1932 Olympics. Women's soccer has been held in every Summer Olympics since Atlanta 1996.
Yes, soccer is a national sport. In fact, it is the most widely popular sport in the world, and almost every country has a league of some sort and participates in the World Cup, the biggest sporting event in the world (The Olympics may be too).
Yes. Football (soccer) has been played in every Summer Olympic games except from the years 1896 and 1932. Football at the Olympics was a sport for men until 1996 when women's football was added to the games.