Taking a break during train trip?

Is it possible to take train between two locations and stop for hour or two (say until next train of same type to my destination) at some station in between without buying separate tickets the two parts of the trip? The way the prices are calculated seems to increase the price of separate tickets compared to combined on by about 10% for each stop, so I would like to know if they are needed? Is there some one day area tickets that could be used for this?

Also is there cheap option for rail pass that includes Tokyo - Kyoto Shinkansen and local JR trains (in Tokyo, Kyoto, Nagano area) for 3 non-consecutive days? All that I have found are either for 7+ days or don't include the Shinkansen, which make them quit poor value options.

Edit: If I'm reading japan-guide.com correctly, over 100km trips would allow stops, as long as there are no supplemental fees on the ticket (or you pay them separately). So can't really use with shinkansen that easily.