That's a bit weird but I'll give it a try!Yes, you have to download C1 if you want to start anew. As for save transfers:
C1 -> C2: You save at the end of C1 when asked, that will be imported into C2 as is.
C2 -> C3: No such function here. You better note down your stats at the end of C2, because you will fill out a questionnaire about the things that happened in your game and you enter the current stats per hand.
C3 -> C4: To be determined, but it seems we are getting the auto-import again.