Let's say that I want to replace the memory card in the camera after a week. I disconnect the digisnap from the camera (because I have to take the camera out of the box) and replace the card. Do I have to reprogram the digisnap or it will continue taking pictures as previously programed?

The cables should be long enough to remove the camera sufficently to remove the card. Once running, as long as you don't disconnect power to the DigiSnap, it should continue forever... regardless if the camera is attached.