Kansai to Higashiyama

No. You can use it to go to Arashiyama in the west, and places like Fushimi Inari in the southeast.

This site can give more info:

http://www.japan-guide.com/e/e2363.html

thankyou , so when i get to Kyoto I will have to go out the station and buy a subway ticket and go back in again to get the subway to Higashiyama. ?

Yes, although the Kyoto subway line won't take you all the way either. You can take a bus, and there is a bus day pass for 500 yen, although in busy tourist seasons it can move rather slowly down the streets.

can I take my case on the bus OK

If you mean suitcase, there is no specific prohibition, but hopefully it is small and can be placed above the seats in the luggage rack. If you travel during morning rush hours you might it extremely difficult to bring it on at all. If it is medium sized or larger, and even a little heavy, it would be much smarter to use a luggage locker at Kyoto Station.

catching the train from Kyoto to Nakatsugawa . If I book a reserved seat On the Nozomi to Nagoya and a reserved seat on the Shinano from Nagoya to Nakatsugawa , I notice you only have 8 min to change trains , if i miss the train do I lose my seat reservation if I get the next train . Also If I book an unreserved seat on the Shinano can this be used on any Shinano to Nakatsugawa without stating a specific train time.

When you make a seat reservation, it is for a given train at a given time only. If you miss your train with the seat reservation, for the next train you'd have to take an unreserved seat.
But there is no booking an unreserved seat on a train - that is why it is unreserved. While unlikely, except at the worst of travel times in a peak season, there's always a chance that you might not be able to sit down at all until someone else arrives at a destination and gets off.