This is correct in that swords were sidearms. Here are several excellent answers concerning Samurai weaponry and warfare: 1, 2, 3, 4.

Here is a thread asking about "why was the sword romanticized".

Kind of, yes. For a long time in Japanese history, warring was done by professional warriors who fought with bows on horseback. That is true. However, this practice began to fall out of favor once massed infantry armed with spears began to become the favored form of fighting. It is true however that horse mounted archery was, and still is, held in high regard in Japan.