Itinerary Check - Help please

Hello,
We are trying to work out which JR PAss is suited for our trip.
We are spending 2 weeks in Japan, but unsure if we should just purchase the 7 day or 14 day pass.
We are staying in Tokyo from the 5th - 10th. To travel around Tokyo is is quite cheap on individual fares, would you recommend purchasing a 7 day pass and then activate the day we leave Tokyo city?
Then travelling to Toyota (what train do we need to catch here? As I have read some of may not be covered under the JR line?)
On the 13th we are then travelling to Kyoto.
Then, Kyoto to Hiroshima on the 15th.

We have found reasonably priced flights from Narito Airport in Tokyo, but we don't know if we will make it there on time if we are travelling back from Hiroshima on the 17th (the day we will fly out). The journey says 11 hours, so we may have to go for a flight instead, but obviously want to make as much use of our JR pass as possible.

Sorry for the many questions! Any advice would be really appreciated!

Thank you