Hokuriku Arch Pass: bullet train Tokyo/Kyoto

We are travelling Tokyo-Kyoto-Tokyo with local 1-day trips to Nara and Osaka from Kyoto. I am wondering if the Hokuriku Arch Pass is a good choice. My main concern is if it covers the bullet (fastest) train from Tokyo to Kyoto? Will it still take us around 2 hours to get there if we purchase the Hokuriku Arch Pass (instead of the full JR pass that is twice as expensive).

We also plan to go to Hakonu, but I believe, none of these passes cover it. Please correct me if I am wrong. Thank you

Will it still take us around 2 hours to get there if we purchase the Hokuriku Arch Pass (instead of the full JR pass that is twice as expensive).

No, it will take about 5 hours.

We also plan to go to Hakonu, but I believe, none of these passes cover it.

Indeed, the trains between Tokyo and Hakone are not covered:
https://www.japan-guide.com/e/e2361_arch.html

Thank you very much!

Hokuriku Arch Pass does not cover the gdirecth Shinkansen route between Tokyo and Kyoto.

You should be fine with just buying individual Shinkansen tickets. To go to Hakone, you can buy the Odakyu Railwayfs Hakone Free Pass, either the version that includes the Shinjuku - Odawara leg, or the gwithin Hakoneh version, depending on where you start from.