How and where to claim a JR pass? what is the JR pass exact time validity and other queries

Hi. Its our first time to go to japan so I have a lot of queries. Our family will be staying in Japan for 13 days. We will arrive on Dec 28 at night. Because 14 days is too expensive for us, we plan to purchase a 7 day JR pass only and will use from Jan 1 to 7.

Questions:
1. If I bought a JR pass today (Dec 27) and we will arrive on Dec 28 but will use a 7 day JR pass on Jan 1 to 7. How and where can we claim the JR pass if we are already in Japan? Mailing of JR pass to our country of origin is no longer possible since we will be leaving on the night of Dec 27.

1. Is 7 day JR pass, valid from 0:00 of Day 1 to 0:00 of Day 8 or depending on the time of purchase? Ex. If i buy a 7 day JR pass on 18:00 of Jan 1, can I use the JR pass until 18:00 of Jan 8?

2. What is the operating hours of bullet trains in Japan?

Thank you so much for your answers.