23 days vacation in September

Hi!
My wife and I will be traveling in Japan for about 23 days (flights not reserved yet), during September (3.9-26.9)
I've done some research, and have the following questions:
The general route looks like (in brackets - number of FULL days we are thinking of staying there):
Tokyo(6)-Nikko(3)-Alps(3)-Kyoto(2)+Nara(1)-Osaka(3)-Hiroshima+Miajima+shimanami kaido (3)
1. Can anyone recommend on a site displaying festivals in September? I couldn't find any major ones in September, and would maybe change our itinerary to match something if it's interesting enough..
2. Mount Fuji climb - how often the weather in September permits the climb?
3. in case we won't go to
5. hakone vs. Nikko - they sound to me "pretty much alike". If we wish to put more emphasis on hikes - is Nikko the best?
6. How should I arrange the order of the itinerary locations, in order to minimize JR pass costs/drive time?
7. Should we rent a cat in the alps, or use public transport? we wish to do Kiso Valley and Kamakochi.

Nikko over Hakone - three days if you are hiking, otherwise what are you doing for three days. Hakone is a "tourist trap" and there are better places to visit.
Osaka - what are you actually doing there? Spend the time in Kyoto, or anywhere else interesting.

Personally, I also think you are spending too much time in Tokyo (you could spend months there easily though), but going to big cities can be done in a lot of other places. japan has so many unique places to experience.

Can anyone recommend on a site displaying festivals in September? I couldn't find any major ones in September, and would maybe change our itinerary to match something if it's interesting enough..

I've been in September and there are some great summer festivals still going on. Katakai Matsuri near Nagaoka features a lengthy fireworks show. In Mitaka, Tokyo, festival participants carry mikoshi up and down the streets throughout the entire day. There is also some interesting processions and horse archery at Kamakura during a weekend in September. These are just off the top of my head.

For researching festivals I do have my preferred websites boomarked somewhere else, but for now I could always recall the most comprehensive one that I know of.

https://www.jnto.go.jp/eng/pdf/newsletter.html

Hello,

I wouldn't recommend you driving in Japan.
Because in Japan, Trains are everywhere and will take you anywhere, and some of my friends who went to Japan had a hard time driving on Left-side when in the US, it's right-sided.

The order of trips looks well-ordered to me.
But I don't think you would need six days to complete Tokyo, maybe 4~5 days is enough.
Instead, you should use that 1~2 extra day to stay longer in Osaka, since they have better foods than Tokyo.

I just wanted to say that it really depends on your own interests! In my opinion 6days in Tokyo is not too much! I`m living in Tokyo for almost 10years now and love the variety!
My parents spent 10 days here in Tokyo and everyday we did something special and different from the day before, that time passed by so fast. But as I said, it depends on so maby factors, if you love nature. of course other places are recommended, but some people do like some tourist stuff and for these people Tokyo is great!
Anyway wish you a nice stay :)