Your current itinerary includes some parts each of which sounds hectic for the first-time Japan travelers.
What is important in choosing places to visit may depend on interests and purposes, but for example, if you discard Nagano you can have more time in Matsumoto, and if you pass Osaka you may have more time in Kyoto.
Arrival in Tokyo 5am (Full day in Tokyo) Flight at 11:10am from Tokyo Narita So, you will come into Japan via Haneda Airport [HND] and go out via Narita Airport [NRT], right?
If you don't have airport option of Kansai [KIX] / Centrair [NGO]
and if your dates with football matches cannot be changed
and if you use railroad every time when it is convenient,
then your trips will be worth purchasing a 14-day Japan Rail Pass.
If you are OK to take overnight buses to travel, for example, between Nagoya and Yokohama,
then a 7-day Japan Rail Pass could be enough and the total cost for accommodation and transportation might be lower.
(By the way, although Narita International Airport is actually NOT located in Tokyo metropolis, it is sometimes regarded as a Tokyo airport. Its old official name included "Tokyo" but its current official name does not.)
[JRP and train seat reservation]
Please note that Travel Service Center in HND international terminal is not open until 11:00.
Your plane is scheduled to arrive early at 5:00, so probably you can reach Tokyo Station by 8:00 at latest, where two exchange offices are open from 7:30. Consult one of them about your seat reservation in trains on JR lines.
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http://www.japanrailpass.net/eng/en009.html# Route from HND to Tokyo Station (requiring about 30 minutes)
Haneda Airport International Building --[Tokyo Monorail, 470 yen]-- Hamamatsucho : gate --[walk]-- gate : Hamamatsucho : Track 2 --[Yamanote Line's inner loop, 150 yen]-- Track 4: Tokyo.
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http://www.jreast.co.jp/e/stations/e1039.html: In Tokyo Station, going down a staircase near the end of platform in your train's direction, you will be on the north pathway. Walking as the track number increases, you will find Yaesu North Ticket gate.
: Or, you can use an escalator in the middle of platform to the central pathway, which leads to Yaesu Central Ticket gate.
[Japan Rail Pass duration]
You can set your Kamakura trip and Hakone trip during the 14 calendar days of your JRP and your Tokyo trips and Nikko trip during other calendar days.
[Bus reservation]
You may have to make reservation of some buses, but reservation centers will be closed when you get to Takayama. I recommend making reservation in advance on a phone call, for example from a reception desk of your hotel in Nagoya.
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http://www.nouhibus.co.jp/english/shirakawago_kanazawa.html[Hakone trip]
If you stay overnight in Hakone area, a 2-day Hakone Free Pass (3900 yen version) might be a good option.
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http://www.japan-guide.com/e/e2358_008.html[Nikko trip]
A World Heritage Pass and an All Nikko Pass sound worth considering.
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http://www.japan-guide.com/e/e2358_002.html[Koyasan trip]
A 2-day Koyasan World Heritage Ticket might be a good option.
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http://www.japan-guide.com/e/e2358_012.htmlYou can make transfers Shin-Imamiya Station. The leg Shin-Imamiya -- Gokurakubashi -- Koyasan is operated by Nankai and NOT covered by a Japan Rail Pass.
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http://www.japan-guide.com/e/e4904.html (Select "To/From Nara")
[Osaka trip]
In Shin-Imamiya Station of JR-West, trains running for Osaka Station are using Track 3.
You will allow very short time for Osaka, so I recommend checking in advance location of Osaka Station, Umeda Stations of Hanshin and of Hankyu and some department stores.
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http://www.japan-guide.com/e/e4009.htmlNote that you cannot take a Shinkansen super-express train from Osaka Station. You can take a non-Shinkansen train from Track 7, 8, 9 or 10 in Osaka Station and reach the next Shin-Osaka Station within a few minutes.
In Shin-Osaka Station you will not have to get out and come in through gates, because you can pass through a Shinkansen transfer gate to the Shinkansen zone. (Search for "Shinkansen" on sign boards.) This transfer may require about 10 to 15 minutes.
[For your information: first snowfall]
# Average of dates when the season's first snowfall was observed during 1981 - 2010
November 21: Nagano;
November 29: Kanazawa;
December 11: Hiroshima;
December 15: Kyoto;
December 20: Nagoya;
December 22: Osaka;
January 03: Tokyo;
January 07: Yokohama.
