JR East Pass coverage

It is not very clear about the coverage of the JR East Pass on the website. Would like to check:
1. Is the East Pass valid for NEX?
2. I want to go to Matsumoto. The Hokuriku Shinkansen is covered by the pass to Nagano. What about from Nagano to Matsumoto? Is the train ride also covered?
3. As an option, is the Chuo line Azusa trains also covered by the pass? Is it better to take the Azusa to Matsumoto directly?
4. I will be traveling on Oct 9 which is a holiday in Japan. Will the train be less frequent? Do I need to book in advance?
Can I book with a JR East pass?
5. Does the HyperDia site provide timetables for the above?

Advice much appreciated!