The CityPass is a plastic card with a barcode, and can be taken directly to the turnstiles where they will take your photo and print the actual ticket that is used for FastPass machines, etc. No need to go to Guest Relations. So yes, each person must present their CityPass at the turnstile to enter.
OK, then you do need to go to Guest Relations. (I presume you bought directly from Disney). So yes, the person with the credit card used needs to go pick them up, and only that person.
Ticket booths can take care of you, I would also try to upgrade the 3 day to a 4 day...itd be like $20 a ticket for an extra day.i looked it up....3 day hopper is $295 4 day $320 5 day $335...so they would pro rate the value of the Disneyland ticket at $295 and charge the difference to upgrade. We have done this and was an amazing value