Thank you for all of these screenshots. Upon further inspection, my card didn't show up in the app even though it was on my account. Yesterday, I put in the number on the card to the app and it said it was already linked. Today when it wasn't there, I tried to do it again and this time it said the number was invalid. So, I talked to a Disney person and apparently, the card number that I have online isn't the same as the card number that we will have on the actual card once it is activated, so there isn't a way to link it to the parks app until we have the actual card in hand. He told me that we won't be able to apply a discount until the card has been activated on our first visit. We can purchase MB with the AP discount once the card is activated and we are in the parks. The included bands can only be shipped after the AP is activated and those will arrive after our trip. So it seems the only option to have MB at a discounted rate is to wait until we get there. I put in the suggestion that AP holders can select their delivery date of their included magic bands. Maybe if enough people put in the request, Disney will listen.
I also asked about the hole punch thing, just to make sure it wouldn't damage the cards or anything. He said it should be fine. Thank you everyone for your replies!