Bullet train inquiry

Hello,
Our entry destination is Fukuoka. Will spend 2 days in fukuoka and go to Tokyo after. Will spend 2 days again in Tokyo and then after that will go to Mt. Fuji and will spend overnight. then go back to Fujioka until our return to the Philippines. We are tourists.
My question is do we need to avail of the bullet train? If yes, if we are travelling March 29 to - April 5, 2018, can we buy now the ticket? Is 7day pass recommended? Can i request for the bullet train schedules?

Appreciate your reply on this. Thank you.