JR pass from Odawara

Hi,

We are planning to visit the Hakone area after visiting Tokyo and from there we'll continue to Kyoto. Because of this, we're planning to purchase the Hakone Free Pass at Odawara Station.

My questions are:

1. Can we operate the JR pass (for the first time) at Odawara station ?
2. Are there many JR trains to Kyoto (from Odawara) or is it better to go back to Tokyo and from there to take a JR train to Kyoto?

Thank you in advance. - Yael

Can we operate the JR pass (for the first time) at Odawara station ?

Operate a pass? I am not sure what you mean. You can exchange the Japan Rail Pass at Odawara or exchange it in advance at some other station and then start using it from Odawara. Other stations that allow exchanges:
http://www.japanrailpass.net/eng/en009.html

Are there many JR trains to Kyoto (from Odawara) or is it better to go back to Tokyo and from there to take a JR train to Kyoto?

There are direct hikari trains once every two hours. They are the best way for Japan Rail Pass holders to travel from Odawara to Kyoto. Next best connections could be kodama-hikari combinations via Atami, Mishima, Nagoya or Shin-Yokohama. You can look them up here by excluding nozomi trains from results:
http://www.japanrailpass.net/eng/en009.html