when i download the next update do i delete the 0.3 version and redownload the whole game again? does my save carry over?
For PC, you can delete old version if you want to. Your saves are stored in different place so no need to worry about it.
For Android, you need to overwrite the installed app and not uninstall>install it. That way, your saves won't be affected.
In both cases, you need to re-download the game.
just to be clear — it’s safe to delete the whole folder? Where is the save stored?
Yes, it's completely safe to delete whole folder. Pretty sure saves are usually stored in AppData folder.