Lost in JR system and paths

Hello all! This is going to be my very first trip to Japan as well as my first solo trip (female, early 20s). I will be gone for ~1 month. After much research, I have settled on the cities I will be visiting and the approximate time spent in each. However, I am still very lost in several things. If anyone can help out, I would be SOOOO grateful. I have tried my best in everything and appreciate any advice given :)

(1) I am HIGHLY confused on the "path" that I should take, meaning the order of the cities to visit. I am flying into Tokyo.
Would this path be best?:

tokyo [5-7 days] --- matsumoto [1 day] --- takayama [1-2 days]--- kanazawa [1-2 days] --- nagoya [pit stop (few hours)] --- kyoto [3-4 days] --- osaka [1 day] --- kobe [pit stop (few hours)]--- nara [1 day] --- koyasan [2 days (overnight temple stay)] --- himeji (castle) [1 day] --- hiroshima --- fukuoka [1 day (night visit)]
I would have preferred to travel straight from Tokyo to Kyoto then Nara, but that means traveling back up again and continuing the path stated up above. Would this be silly to do?

(2) Are my days spent wisely? I am a decently/semi fast-paced traveler, meaning I do not need to travel at a very leisurely pace. I prefer more rapid travel than getting bored in a city and still having hours/days remaining.

(3) After much reading, I believe the Japan Railway Pass would best suit my itinerary! Thus, I was thinking of buying the JR pass (21 day) and activating it when I leave Tokyo. However, since I will be in Tokyo for ~1 week, I will purchase a Pasmo for that time. Is this a wise idea? I am not exactly sure of the difference between a Pasmo vs Suica-NEX pass though. In addition, when I leave Tokyo, would I return the Pasmo to receive back the down-payment? Or would I need the Pasmo in the other cities I am visiting? Would it be best to travel back to Tokyo to fly out, therefore also being able to return the Pasmo, or do I fly out from Fukuoka?

Thank you thank you thank you to all who help!

tokyo [5-7 days] --- matsumoto [1 day] --- takayama [1-2 days]--- kanazawa [1-2 days] --- nagoya [pit stop (few hours)] --- kyoto [3-4 days] --- osaka [1 day] --- kobe [pit stop (few hours)]--- nara [1 day] --- koyasan [2 days (overnight temple stay)] --- himeji (castle) [1 day] --- hiroshima --- fukuoka [1 day (night visit)]
I would have preferred to travel straight from Tokyo to Kyoto then Nara, but that means traveling back up again and continuing the path stated up above. Would this be silly to do?

Looks a bit complex to do that sequence at the beginning. What about:
Tokyo and then head straight to Kanazawa by shinkansen.
Takayama is easier to get to from Kanazawa.
From Takayama, head to Nagoya (there are some good /cheap accommodation options there and do Matsumoto as a day trip.
Kyoto could be a good base to do Nara and Osaka rather than changing hotels all the time.
For the lower portion, as you are doing Kobe as a pass-though, why wouldn't you do the same for Himeji Castle (i.e. as a day trip from one of your other locations).
Hiroshima and Fukuoka I assume you are flying out from there.

As for back-tracking, don't worry about that too much - the trains are quick on the main line.

Japan rail pass is valid for continuous calendar days so even if you do not use it in your itinerary, you will spend your precious JR pass days without using it. So, in general you will plan your travel so that you can maximize the JR pass to travel as much as possible in your JR pass days.

I think the two most "touristic" places in Japan are "around Tokyo" and "Kansai region including Kyoto, Osaka, Nara, Kobe and Koyasan". In these areas, you will not need to use JR pass which is good for long distance travel. So, considering your relatively long time travel (about one month), you should start using JR pass when you leave Tokyo to Kansai (via Matsumoto, Kanazawa, Hiroshima etc) and end up your long distance travel in Kansai (or vice versa). If you land in Tokyo you might better leave from Kansai airport. I think 7days pass will suffice for your itinerary (Tokyo Matsumoto Takayama Kanazawa Hiroshima Fukuoka Osaka). Of course you can add 30000 yen to buy 21 days pass which will give you more freedom in your itinerary (for example, you can travel from Kyoto to Mishima via Shinkansen to see Mt Fuji when the weather is fine in your Kyoto days).