17 days itinerary

Hi

I will be visiting japan next october 2016 to spend my birthday and get to know the country.
I have been trying to fit as much as I can to the 17 day itenerary but i have some doubts, most if them concerning the middle of my trip (Takayama, Nagano and Yudanaka).

The itenerary that I was think about would be:
Day 1 - fly to Japan
Day 2 - arrive at Osaka in early morning and go to Kyoto to start exploring and stay there
Day 3 and 4 - Kyoto
Day 5 - day trip to Osaka Universal Studios (it's my birthday 😃)
Day 6 - day trip to Nara
Day 7 - day trip to Hiroshima and  Miyajima
Day 8- go to Mount Koya and stay there at buddist temple
Day 9 - go to Osaka and stay there
Day 10- go to Takayama and stay there
Day 11- go to Shirakawa Go and then go to Tokyo and stay there
Day 12- day trip to Nagano and to the snow monkey park
Day 13- day trip to Nikko
Day 14-16 - Tokyo
Day 17 - fly home from Tokyo in the morning

My doubts are:
1) Is this plan feasible? I haven't seen any plan like it and i know that it is a little ambitious.. would you rearrange it any other way?
2) I heard about Himeji castle. Should I see this castle instead of Osaka or Kyoto castle?
3) if i don't see the peace memorial museum is it enough to do a day trip to Hiroshima and Miyajima?
4) Should I stop by Seki to see the samaurai sword museum before going to Takayama? Is it worth it?
5) Do you have any recommendation of good ryokans to stay at Takayama that serve hida beef for dinner?
6) Is there an onsen with and outdoor mixed bath in Takayama? Or should I go from Takayama to Yudanaka (instead of going to Tokyo) and stay at an onsen in Shibu? Or do you think i will have the time to go to an onsen in Shibu i The day trip and then get back to
7) Is the trip to Yudanaka worth it in the beginning of october? Is it probable that The monkeys will be there?

Can you give me some feedback on this topics?

Regards
Sofia

Generally points about your itinerary.
You are going to Osaka to Kyoto, Kyoto to Osaka, Mt Koya to Osaka.
Stop visiting Osaka in parts, do it in one go. Osaka has some things to do in the day like the aquarium, castle, and USJ. However, it becomes alive at night with the shopping and food around Namba/Tennoji/Shinsekai.

I am not certain as to your travel pace but unless a fast pace traveler, your one day to Hiroshima is not sufficient time.

Answers to
1)
I would head straight to Kyoto from the airport and only visit Osaka for USJ.
There is not sufficient things to do in Takayama. I would rather head to Kanazawa and spend a morning (or half a morning) in Takayama.
You can take the shinkansen from Kanazawa to Nagano. No need to go to Tokyo and then back to Nagano just to go back to Tokyo. Either make a day trip from Kanazawa or do it on the way to Tokyo.

2)
Kyoto castle is not ....
Kyoto is more known for the traditional/historic/beautiful streets/buildings/temples/shrines/gardens. Himeji castle is more pretty than Osaka. Though considering the time it takes to get there, it may be better just to go to Osaka or not see a castle at all. (Castles in Japan are more for photo taking than actually entering and exploring)

3)
What else would you be doing in Hiroshima besides the peace memorial? It is one of the key attractions. Hiroshima castle? Mazda museum? If I had time for only one thing in Hiroshima, I would do the peace memorial.
Regard to time, it really depends on what you want to do. From Hiroshima to Miyajima and back would take about 3-4 hours. (Take the cable car to the top, do not walk) Returning to Hiroshima you would have time to see one or two sights before heading back to Kansai.

4)
Can't help you here.

5)
I can't help you here. Do email the ryokans whether they serve such cuisine. Most will as it is the local specialty.

6)
I would stay in Kaga onsen if time permits. If not a hotel at Nagano would be great too.

7)
They usually come out in winter. Though October has a chance still.

Thanks you so much for your comments.
This is my first time visiting Japan and reading your reply helped a lot.

In the day that I go to USJ i'll try to go to Namba at night if i got the time.

I'm thinking about changing the itenerary from day 7 to 12.

Day 7 - go to Mount Koya and stay there at buddist temple
Day 8 - go to Hiroshima and then Miyajima and stay there
Day 9 - Miyajima/Himeji and stay at Kaga onsen?
Day 10 - morning in Kaga Onsen and trip to Kanazawa
Day 11- Go to Takayama in the morning and then to Shirakawa Go
Day 12- either bullet train to nagano or going to tokyo if there are no snow monkeys.

Do you know any free apps that identify the best itenerary and hour for people with JR Pass?
I've read about hyperdia but you have to pay to get the best JR Pass itenerary..
I'm concerned about the time i can get from Mount Koya to Hiroshima and from Himeji to Takayama.

Do you think I will be able to Go on a day trip to see a bit of Takayama in the morning and then go to Shirakawa Go?

You don't have to pay Hyperdia for anything. Just use their web page and not the app. You may have to expand and retract if using a smart phone, but that's better than paying money for the same information.

You can also use google maps to check journey times and distances.

Hyperdia is better, but you have to know the exact names of the stations for it to work correctly.