what's the best website to buy JR?
There is no JR officially-recognized website to sell or buy a Japan Rail Pass.
The issuer of Japan Rail Passes (= the six JR regional companies) requests you to visit a real office and listen to the explanation regarding the eligibility. http://japanrailpass.net/en/purchase.htmlhow much time before going to Japan is best to buy? is there refund in the case of trip deletion?
You can check the related information on the official website. http://japanrailpass.net/en/about_jrp.html
Once you have started using your Japan Rail Pass, there is no refund,
even if the train service which you use / could have used is delayed / suspended.
Your Exchange Order should be turned in for a Japan Rail Pass within 3 months from the day of purchase.
When you receive your Japan Rail Pass,
you specify the day within 1 month when you start using the pass,
and the pass should be valid from that day. In the case I have to modify itinerary during the holiday, can I delete the train booking and book another train short time before the departure?
Regarding your JR train ride with your Japan Rail Pass, basically you can renew your seat reservation before the scheduled departure time.
When you travel with JR regular tickets,
you can once replace your reserved-seat ticket before the scheduled departure time;
to cancel the ticket after the replacement, you should pay a handling fee.
(Even after you missed your train, it is recommendable that you get nullified your seat reservation so that another passenger can reserve the seat.) what are the websites to book trains and seats?
That depends on JR sections.
JR-East manages its own website
for foreign passengers who hold a credit card of a designated brand
(including passengers who plan to travel with Japan Rail Pass)
to reserve seats of trains for Shinkansen
(other than Tokaido, Sanyo and Kyushu Shinkansen) sections
and of Limited Express trains for JR-East and JR-Hokkaido major sections.
This JR-East reservation system requires you to pick up your tickets by 21:00 (Japan Standard Time) on the day before your boarding day; so it works mostly for your train rides on Day 2 or later. https://www.eki-net.com/pc/jreast-shinkansen-reservation/English/wb/co...https://www.jreast.co.jp/e/ticket/reservation.html
Regarding other JR sections, there seems to be no JR official reservation website designed for Japan Rail Pass travelers.