Using the JR Pass within and between cities...

I am arriving to Narita Airport on April 1st. I will be spending the night in Tokyo and then headed to Hiroshima on the 2nd. I will then make my way back during the week while I make stops at Kyoto, Kawaguchiko, and then reach Tokyo on April the 6th. I won't be flying out until the evening of the 9th from Narita.

Should I pay for a one way ticket from Narita to Shinjuku and then activate my pass the 2nd to make all of my longer trips on the pass?

Then I have three days in Tokyo and read that I am not going to be able to use my pass for the subway system? How much extra is the subway passes?

Thank you for your assistance :)