JR-Pass: 1 week / 2 weeks / No?

Hi everyone,
Another JR-pass question, hope someone can be so kind to advice us.

We are travelling to Japan for the first time and already planned our stays and now would like to know if a JR-pass would be of value.

26 April Osaka>Koyasan
27 April Koyasan>Nara
28 April Nara>Kyoto
((4 days in Kyoto)) 2 May Kyoto>Tokyo
((4 days in Tokyo)) 7 MayTokyo>Osaka
8 May Osaka>Arima>Osaka

The questions:
- JR-pass 2 weeks from 26 april 9 May = €341.00 But does this cover all our travels?

• JR-pass 1 week from 2 May untill 8 May = €214.00 Plus all the costs of 3 travels in April - but i read somewhere that these are very cheap fares, is that true? (This must be better than JR-pass 26 april to 2 May, then we have no JR-pass in Tokyo and have to but a ticket from Tokyo to Osaka and from Osaka returnticket to Arima.)

• Or is it cheaper to just buy seperate tickets for us (no JR-pass)?

• Would the JR-pass also cover a trip to Takayama (made from Tokyo)?

We hope someone can help us with this, we would be very thankful.