Atami to Kyoto

I am staying 6 nights in Atami from 23 - 29 March. How much is the Shinkansen train from Narita Airport to Atami? How do I get to Kyoto from Atami by JR train and do I need to book train ticket in advance and how much does it cost? It will be only a day trip in Kyoto. I will be visiting Mt. Fuji & Hakone also. Where can I purchase the Fuji/Hakone pass in Atami.
Will I be able to see the cherry bloosom during this time? Appreciate your assistance. Thank you.

How much is the Shinkansen train from Narita Airport to Atami?

Narita Airport is not served by shinkansen trains. You will have to change trains in central Tokyo (Tokyo or Shinagawa Station). Fares can be looked up here:
http://grace.hyperdia.com/cgi-english/hyperWeb.cgi

How do I get to Kyoto from Atami by JR train

By Tokaido Shinkansen:
http://www.japan-guide.com/e/e2018.html

do I need to book train ticket in advance and how much does it cost?

Tickets do not need to be booked in advance. You have the choice of reserved seats and unreserved seats. The fare difference is small. You can look them up both at the above website.

Where can I purchase the Fuji/Hakone pass in Atami.

I don't think the Fuji Hakone Pass is available in Atami, because the pass usually only makes sense if you start and end your journey in Tokyo.

Or do you mean the Hakone Free Pass? I don't think that the Hakone Free Pass is available in Atami, because Atami is not covered by the pass.

Will I be able to see the cherry bloosom during this time?

If they happen to bloom much earlier than usual, you might be able to view them.