Hello OJ,
It's hard to say how to split your days exactly as you will certainly have your own preferences and places you wish to see. However in general I would recommend spending the larger part of your time in Japan in Osaka and Kyoto as they have by far the most to offer. Himeji is great for a day trip and Nagoya maybe a day or two.
As for the JR Pass, it will be close but I think that it would be best to buy normal tickets as you travel. A one way Nagoya - Osaka is ¥ 6,350 which is by far the more expensive part. Travel between Kyoto, Kobe, Himeji and Osaka does not have to be pricey at all since you can use rapid train services that only require fare for local trains.
Hope this helps!
Daniel