Negative.
He's known as "the first samurai" because after helping his cousin through the Gempei Wars he was betrayed because he could have overthrown him (if he wanted). He was the first to committ seppuku, and pwns all.
Minamoto yoritomo was the first ever shogun in japan
Minamoto Yoritomo was never referred to as Shogun during his lifetime. Minamoto Sanetomo was the first man to be recognized as shogun during his actual lifetime.
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A civil war between the Taira and Minamoto clans
In real life the Taira and the Minamoto clans were the two strongest clans of the 4. The other two were the Tachibana clans and the Fujiwara clans.
The emperor was too indulged in court life.
Minamoto no Saneakira was born in 910.
Minamoto no Yoshitsuna died in 1134.
Minamoto no Yoshitsune was born in 1159.
Minamoto no Yoshitsune died in 1189.
Minamoto no Yorinobu was born in 968.
Minamoto no Yorinobu died in 1048.
Minamoto no Yorimasa died in 1180.
Minamoto no Yorimasa was born in 1106.
Minamoto no Noriyori was born in 1156.
Minamoto no Noriyori died in 1193.
Sumika Minamoto was born in 1979.