1) I donft think a pass will pay off. You are 8 days in Kansai area so canft fit the travel Tokyo / Kyoto in a 7 day window.
2) are you traveling alone or with muktiple people. If alone i would go with non reserved seat between Tokyo and Kyoto. (As I am wrtiting this I am somewhere behind Nagoya in a non reserved seat in a Nozomi Shinkansen). The only exception I would make regarding unreserved, I would go reserved if you travel between 31dec and 9 Jan on the Shinkansen.
Anyway you can get a reserved seat and change it when you are at the station to an earlier train or go unreserved. So normally no need to wait for trains. Eg today in Osaka I had a 5 min wait to get into my unreserved seat. And in my way to Osaka on Tuesday I came Dian to the platform in the very minute the train arrived, had time to buy a drink and jump on. Not buying a JR pass also means you can take Nozomi Shinkansen which are more frequent and faster.
3) renting a car for long distance travel makes no sense in Japan. Speed limits are low (maybe 100 km/h) while trains are fast and frequent. Renting a car does make sense if you go to remote areas or want to travel around remote areas. So potentially IN Kawaguchiko renting a car for 1 day can make sense if you want to go to some dater flung places (eg all 5 lakes). I am
a bit worried though about snow. Not sure if there will be snow in the villages / cities at the base of mt Fuji. The mountain itself is already well covered in snow since a few weeks.
4) yes there are some subway passes for x days (I donft know the details but there is a good page on JG that explains all passes. HOWEVER this ticket is only valid on gTokyo Metroh which is one of many rail companies in Tokyo. For many tourists this and the JR Yamanote line is likely the only trains you are going to use. I personally would just get a PASMO/Suica card, which is a card you can charge and use on the go. Itfs also valid in Kyoto, Osaka etc. essentially itfs valid nation wide with some small exceptions.
3 ) the best you can get is data. You canft get a local phone number w/o being a resident. Nor would I know why you need a phone number. If you want to call someone on a landline, just get some Skype credit. Easy and cheap.
4) Ifd expect the shops in Kappabashi doro to be closed but everything else open and specially Meiji Jingu very full of people. But thatfs part of the experience.
6) I donft know why you decided to stay 2 days in Kawaguchiko. What you can do there is look at the mountain from several lakes, and go to an onsen (and look at Mt Fuji). If there is no snow /good weather you could potentially also cycle. Depending on your strength if you can do only 1 of the 5 lakes, I suggest Yamanakako.
That was me there at end if October:
http://bicycletraveljapan.blogspot.com/2022/10/fuji-4-lakes-d1.html8) for the sim, I would buy after arrival eg at a Bic Camera store. For JR pass if you finally decide to buy one, I remember it is cheaper to buy abroad. It wasnft possible to buy in Japan but I think recently it has become available.
9) yes, kindoff. Itfs good to find the fastest connection but sometimes those connections donft make sense (too much changing) or gforcesh you on a Shinkansen when there is a cheaper local train. But yes. In general terms it works.
10) ask you Tokyo hotel if they can keep it for you. But youfll be away for a long time. 11 days (?). So that might be difficult. Two options: (1) pack lighter and donft have stuff you need to leave behind (check if your hotel has a washing machine) or (2) ship your luggage to Kyoto and the back from Kyoto to Tokyo. Yamato Kuroneko will keep your luggage for a few days (I remember Max 7 days) , so you can go with a small bag to Kawaguchiko
Other comments:
In principle you donft need to change hotels between Osaka and Kyoto they are close enough. And I still have to find anything interesting to do in Osaka. Just spent there the day today and went walking in Minoo and then to a super sento, which is nice, but frankly Kyoto, Nara, Biwako are so much better.
If normally you arenft a lot of a planner there isnft any reason to become a planner for Japan. Buy a guide book or use Japan Guide webpage. Look at the weather forecast and plan day by day.
However around NY stay in a big city or in a hotel booked WITH lunch & dinner as many places will be closed. I would also suggest to precook accommodation between 31/dec and 9/Jan.
You are going from Kyoto to Kawaguchiko. On a map that looks reasonable. In reality not so much. I would make it a trip from Tokyo and frankly Ifd make it a day trip as you donft seem to have specific plans beyond glooking at Mt Fujih. Which isnft guaranteed due to weather, so better have some flexibility.