Short answers, pulled from the story.
Tokugawa Ieyasu was a Japanese samurai and daimyo born on the 31st of January, 1543, who became the founder and first shogun of the Tokugawa shogunate. The government he established ruled Japan from 1603 until the Meiji Restoration in 1868, making his political settlement one of the longest-lasting in Japanese history. He is regarded as the third of Japan's three Great Unifiers, alongside Oda Nobunaga and Toyotomi Hideyoshi.
Ieyasu was appointed shogun by the emperor in 1603, three years after seizing power following the Battle of Sekigahara in 1600. He had built his position over decades as the most powerful daimyo in Japan, serving as one of the five regents for the young Toyotomi Hideyori after Hideyoshi's death in 1598. He voluntarily resigned the title in 1605 in favor of his son Tokugawa Hidetada, establishing that the shogunate was a hereditary Tokugawa office, though he retained real control of government until his death in 1616.
The bakuhan system was a governing structure Ieyasu implemented to maintain peace among the daimyo and samurai classes under the Tokugawa shogunate. It used precisely graded rewards and punishments to encourage, or compel, those classes to coexist without conflict. The system endured as the foundation of Tokugawa rule throughout the shogunate's existence until 1868.
Ieyasu, then named Matsudaira Takechiyo, was taken hostage because his father Matsudaira Hirotada sought an alliance with the powerful Imagawa clan against the rival Oda clan. Oda Nobuhide intercepted the hostage transfer and abducted the five-year-old boy. After Hirotada refused to abandon the Imagawa alliance even to save his son, Nobuhide held Takechiyo at the Honshoji Temple in Nagoya for three years, then transferred him to the Imagawa at Sunpu, where he remained until he was in his late teens.
At the Battle of Mikatagahara in early 1573, north of Hamamatsu, the considerably larger Takeda army under Takeda Shingen overwhelmed Ieyasu's forces and inflicted heavy casualties. Ieyasu retreated to his castle, then ordered his men to light torches, beat drums, and leave the gates open, which made the Takeda generals suspect a trap. They camped for the night rather than besieging the castle, and a Tokugawa raid on the camp that night was enough to convince Shingen to abandon the offensive entirely.
The Iga crossing, known as the Shinkun Iga-goe, was a dangerous journey Ieyasu made through Iga Province in June 1582 after learning that the general Akechi Mitsuhide had forced Oda Nobunaga to kill himself at the Honno-ji temple. Stranded in the Kansai region with only a small party, Ieyasu had to cross territory patrolled by Ochimusha-gari, or samurai hunter gangs. According to the Ietada nikki, the group suffered around 200 casualties during the journey and arrived at safety in Mikawa with roughly 34 personnel remaining.