1 month trip in October

Hello,

We are planning a trip to Japan in October. Could someone please check over our itinerary and feel free to provide suggestions to improve it.

Since we will be travelling for 1 month, we need to know when is the best time to activate our JR Japan Pass .
We thought that it would be most judicious to start it on 08/10/17 so that we can use the pass till 28/10/17 but are not completely sure as we don't know what the transport cost will be for the non covered days or places.

below our trip planning:

Itinerary for Japan (30/09/17 - 30/10/17)

Saturday 30/9/2017 departure for Tokyo
Sunday 1/10/2017 arrival in Haneda at 15:50
Monday 2/10/2017 Tokyo
Tuesday 3/10/2017 Tokyo 1 day to have a closer glimpse of Mt Fuji
Wednesday 4/10/2017 Tokyo either at Chureito Pagoda or Hakone
Thursday 5/10/2017 Tokyo
Friday 6/10/2017 Tokyo
Saturday 7/10/2017 Tokyo
Sunday 8/10/2017 departure for Nikko
Monday 9/10/2017 Nikko temples
Tuesday 10/10/2017 Nikko lake
Wednesday 11/10/2017 departure for Nagoya
Thursday 12/10/2017 Nagoya
Friday 13/10/2017 Nagoya these 3 days we want
Saturday 14/10/2017 Nagoya to stay there for the Oshu
Sunday 15/10/2017 Nagoya Nagoya Festival
Monday 16/10/2017 Nagoya
Tuesday 17/10/2017 departure for Takayama
Wednesday 18/10/2017 Takayama 1 day to Shirakawa-go and/or Gokoyama
Thursday 19/10/2017 departure for Kyoto
Friday 20/10/2017 Kyoto
Saturday 21/10/2017 Kyoto
Sunday 22/10/2017 Kyoto Jidai festival
Monday 23/10/2017 departure for Hiroshima Miyajima
Tuesday 24/10/2017 Hiroshima Museum
Wednesday 25/10/2017 départure for Osaka
Thursday 26/10/2017 Osaka Nara
Friday 27/10/2017 Osaka Kobe
Saturday 28/10/2017 Osaka perhaps Mt Koya
Sunday 29/10/2017 Osaka
Monday 30/10/2017 departure for Brussels (at 11:00)

We want to stick to 13+14+15/10 in Nagoya and 22/10 in Kyoto for the festivals.
Can you let us know which part of the journey is not covered by the JR Pass?
Can you also let us know which other passes you recommend us to avoid expensive transport fares?

thanking you in advance and best regards