What JR Pass should I use for my trip?

I am going to Japan and I need a JR Pass that I can use for my different day trips in Japan, preferably just 1 JR Pass. I prefer a 5 or 7 day JR Pass.

Here are the places I will be going to:

1) Matsumoto to Nakasendo Trail
2) Matsumoto to Snow Monkey Park
3) Matsumoto to Kanazawa
4) Kanazawa to Takayama & Hida Furukawa
5) Kanazawa to Toyama
6) Kanazawa to Nagoya*
*6 is not a total need, I prefer to have a JR Pass for 1-5 since those will be my 5 consecutive days

Based on my research, I saw that the trains we will be riding frequently are: JR Shinano Limited Express, Hokuriku Shinkansen, Hida Limited Express, and Shirasagi Limited Express. I considered the JR Takayama-Hokuriku Area Pass but I am not sure if they will cover the Shinano, Hida, and Shirasagi Limited Express trains.

What JR Pass should I get that is best for my day trip train needs?

You can see info on the Takayama-Hokuriku Area Pass at
https://www.japan-guide.com/e/e2361_takayama_hokuriku.html

As you can see, Matsumoto is not covered at all, and in fact there is no JR access to the snow monkeys. Other passes are listed at:
https://www.japan-guide.com/e/e2357.html
It doesn't look like any one pass will fulfill all your travel needs.

Thanks! Can I use this for Matsumoto - Kanazawa or still no because the point of entry is from Matsumoto? For the snow monkeys, I plan to use the Nagaden Snow Monkey express bus.

Alternatively, is there a 3-day JR Pass I can use for my trips to/from Matsumoto?

Please look at the link I gave you above, or look at the JR West page on the pass:
https://touristpass.jp/en/takayama_hokuriku/
There is a pass coverage map, and Matsumoto is not near it. But you can buy a train ticket to Toyama to start using the pass from there.