1) I think I've spotted the issue with the saves. I'm on Android and 0.1.1 has a different name to 0.1.0 it's now called Card Prototype and is a separate installation with its own save folder. I'll copy the old save files to this location and let you know if it makes a difference.
2) To be honest I've not used the reroll option more than a couple of times. I'll start using it and see how that affects game play.
Maybe a reroll option for the card selection (for a cost) would give more chance to get a particular type of card, but at a price.
3) Okay
4) I think this could be done as a new screen that you toggle between. As you say there isn't really space to put it in the current layout.