Hi Goblin,As explained before, the fare on hyperdia is the cost of traveling that distance on JR rail lines. However, this is only the base fare--local trains will cost this much.
Since you are taking a shinkansen, they have supplemental express fee (you are paying extra for the convenience of using a faster train). This fee is the 'charge' you are seeing in Hyperdia. You must pay both the 'fare' and the 'charge' when using the shinkansen. Reserved seats only cost a few hundred yen extra. In hyperdia, if you compare the same search, but with reserved and unreserved seats, the 'fare' stays the same, and the 'charge' is slightly most expensive for the cost of the reservation.
As for purchasing tickets, you can generally do that on the day of travel, unless it is during a busy holiday period. Most times you will find space in the unreserved section, I found.
