Using the JR Pass in Tokyo

Hello ~

I will visit Japan with my family in April, we are planning to stay 6 or 7 days in total and our itinerary is:

April 21st - Arrive at Tokyo Haneda
April 21st ~ April 24th - Travel in Tokyo
April 25th - Shinkansen to Fukuoka
April 26th - Shinkansen from Fukuoka to Hiroshima (only for the day)
April 27th - Departure

I know the JR Pass cover the between-cities Shinkansen trains, but I am still a bit confused if is possible to use it in the regular subway (as long as they are from JR company), what is the difference between the Monorail and the regular subway?
Also, once that I need to take the Shinkansen train, how do I reserve my seats? Do I need to go directly to the ticket booth at the station itself and show the pass to get a ticket?

I hope you can guide me a bit,
Thank you very much :)