Would JR Pass be best option

Hello,
We are a family of four, all adults, who will be in Japan mid December to mid January.

I wonder if for this portion of our travels, if the JR pass would be a good option:

Dec 27 to Jan 2: Tokyo to Kyoto, with day trips to Uji and Fushimi Inari Taisha
Jan 2 to Jan 4: Kyoto to Osaka, one day at Universal
Jan 4 to Jan 8: Hiroshima, and one day/night in Miyajima
Jan 8 back to Tokyo for flight to US on January 9

Also, one of us is currently a US student studying in Japan. After classes end, they will obtain the temporary visitors visa, so I wonder if we do use the JR Pass, can I order it for them while they do not have the temporary visitors visa?

Thank you.