Can I bring my game from a past version to the current one?
Yes, it is possible in all versions.
On Android it happens automaticall
On Widows you have to copy them over
On Mac im not quite sure. I think you just copy them over, just like you do with widows
In Android i just have to install the new version without uninstalling the old one?
Yes, it should find and update the old app on auto.
