If you haven't agreed to take the photo with Anna, Ken's quest ends then and there as far as I'm aware.
If you are asking how to take the photo, it's on Thursday -> Hallway -> Garage -> Entrance and there should be Ken and Anna.
I haven't ever refused Ken buying groceries so I can't help you with what happens if you decline.
I don't think you can manipulate save files easily. I just restart if I've completely screwed something
You can go three ways:
-Start sharing with Anna ('Invite someone' option when in Studio)
-Say that you'll be friends (I forget the actual option, but you'll know what I mean) this also opens sharing with Samantha
-Basically say 'yeah okay bye' and have no more content with Ken
It's been some time so I can't remember exactly the dialogue choices so I could be wrong. I can start a new game to recheck if you really want me to.
