Yes, saves are freely transferrable! It SHOULD be automatic between updates and free/paid versions, though I've never tried going backwards in versions lol.
Glad you're enjoying the game so far!
I was playing the demo, then went and bought it, and there was no issues for me at all. I use windows, but I imagine Android and Mac would have the same thing in regards to saving and updating. Hope you like it as much as I do, it's one of those games that is "oh...it's 2 AM? geez guess I lost track of time" because it's so engrossing!