The JR Railpass is not valid on the NOZOMI Shinkansen which is a type of service on the Tokaido/Sanyo Shinkansen Line. There are other shinkansen trains that run on the Tokaido shinkansen line, which includes the Hikari Shinkansen and Kodama Shinkansen (slowest).

You are free to use the Hikari Shinkansens between Tokyo and Kyoto. If you go out to Himeji you might have to connect at Shin-Osaka station (one station after Kyoto Station via Shinkansen).

Also as noted, get a 7 day railpass and because you are on a 9 day trip, pay single fare tickets the first few days in Tokyo then "activate" the railpass on day 3 or whenever you plan to depart for Kyoto, since it will make the railpass "economical" to use because it will cover your return trip too.

When you exchange your JR Pass voucher for the actual pass, you can indicate what day you wish to start using the pass.

As noted, the JR Railpass is only valid on JR trains, so it is not valid on subways, monorails, other private rail lines, etc.

Kyoto is well covered by a dense network of buses so getting a day bus pass in Kyoto is a must in my opinion.