Question about duration of JR Pass

This may be a simple question but say if I get a 7 day JR Pass, and I get it at 16:00 on the 10th, does it last until 16:00 on the 17th? or the end of the day on the 17th?

Also if say it expires at 16:00, does that mean I'm able to get on a train that departs at 15:59 and arrives later than 16:00? or do I need to arrive before the time?

Thanks

The Japan Rail Pass is based on calendar days, so if you activate it on the 10th at 16:00 it will expire on the 16th at 24:00.

You can board trains that depart at 23:59 on the 16th and the pass will cover your entire journey except for additional supplements (ltd express fees, shinkansen) that you might encounter if you transfer after midnight.

More info here:
http://www.japan-guide.com/e/e2361.html

if I get a 7 day JR Pass, and I get it at 16:00 on the 10th, does it last until 16:00 on the 17th? or the end of the day on the 17th?

Neither.

Duration of validity of a Japan Rail Pass is counted not from the moment when you get it but according to calendar days from the day which you designate when you get it.

When you turn in your Exchange Order (purchased outside Japan) for your Japan Rail Pass, you have to designate the same day or a later day within one month as the first day of its validity.
If you get a 7-day Japan Rail Pass designating 10 September 2014 as the first day, basically it will be valid until the end of 16 September 2014.

do I need to arrive before the time?

If the end of the last day of validity comes while you are traveling with your Japan Rail Pass, it can exceptionally cover basic fares until you first exit JR through a gate, but it cannot cover an additional charge concerning a later train. So, you can take Local trains with that Japan Rail Pass before exiting JR, but you cannot take a later Express, Limited Express or Shinkansen super-express train even if you are still inside JR gates.

Among railroad fees in Japan, there is a fee which is required regardless of train services and called a basic fare, a base fare or so, and there is an additional fee which is required for a specific train service as a service charge.
Regarding JR train services, Local and most Rapid trains can be taken at payment of a basic fare, while an additional charge is required for Express, Limited Express and Shinkansen super-express services.