JR Pass

Hi there, we will be catching trains between October 15 and October 21 Kii Katsuura to Kyoto via Osaka; Kyoto to Hiroshima return via fast train; Kyoto to Tokyo, with potential for day trips on trains in this time.
I believe it will be economical to purchase a 7 day JR National Pass?
Does it activate the seven days from the first trip or when you purchase the pass do you specify the dates? Would the pass be from midnight on the first date or from the time of the first trip?
As we will not arrive to Japan until October 9th, is this when we can reserve seats on particular trains? Or are we able to book any train tickets from Australia when we receive our exchange order or do we have to wait until in Japan?
We are concerned about not being able to book in advance as the train from Kii Katsuura only leaves once in the morning, which we cannot. miss and also we have booked a day trip in Hiroshima and we will need to get there by train and would like to reserve.
Do these trains become fully booked or will it be fine to book on the day or on arrival into Japan? Are you able to do the bookings and seat reservations on line, or do you have to do them at the train stations?
Thanks so much for your assistance!