The game is really great, one of the best I've played in a long time. On the next update though, how can I play v0.6.6? Do I download the entire v0.6.6 apk and remove the v0.6.5 apk? If that's the case will I have to play the entire game again?
I'm super glad you're enjoying it so far!
When a new version is released, just download it, and when you attempt to open it it'll ask you to update the one you already have installed. Do that and your saves will be fine and can continue from where you left off.
DO NOT delete your old version before you download the new one. Or else yes, you will have to start again.