Moonges,(1)What is the minimum time needed to reserve a seat?
You can reserve seats right up to the time of departure, but of course you need to allow a few minutes to get from the ticket office to the platform. If the ticket office is busy, it can sometimes take as long as 10 minutes.
(2)What happens if I miss the train that I've reserved (I will have a JR pass)?
There is no penalty or anything, but it means that someone else may have to stand despite there being a vacant seat, so you should make the effort to catch the train you are reserved on or else return the unused seat reservation to the ticket counter so that the seat can be released for someone else further down the line.