Unfortunately you are incorrect on several of these points.
First, you do not go into the park, you go to the will call window outside the park - it is one of the ticket booths, or in the case of the MK entrance, usually the Guest Relations window. You turn in your GAD voucher there, provide proof (photo ID, multi-day ticket) and choose the FP option.
More details on the card and how to use to can be found
here.
It sounds like you are remember the Dream Fastpass, one of the prizes during the Year Of A Million Dreams, which had the break-off tabs on the sides. They don't use those any more.
For your question specifically, there is no set number that Disney will tell us. They will only say that they MAY run out, and they MAY not give them out after 11am, although no one has reported problems getting them later in the day.
For ONE voucher, all four of you will get a FPXC, so long as all of you are present at the will call window. So you can take your three vouchers and do the same on different days at the same or different parks. Some have talked about using more than one at the same park, although it is uncertain if the CM will balk at giving out more than one set to a group.