Well, yes if you're using the itch.io launcher you can download the game with it and afterwards when you update the game it will download only the changes. Very neat thing.
Saves are always compatible, very rarely they're not but to ensure your saves will keep working try saving in a "safe location" like the protagonist's bedroom.
Also you can delete the old versions of the game no problem, the saves are kept on a separate location in
%appdata%\RenPy\CorruptedKingdoms-1547378918
Viewing post in Corrupted Kingdoms (NSFW 18+) comments
I would try first downloading the version of the game that your saves were under in the launcher. Then go to the save games folder in the version that has your saves, select to copy the game save files, open the save game folder for the one downloaded through the launcher, and pasting them into the folder. Then open the game through the launcher, open the last save you had. If it works then create a new save and exit the game. Then download the newest version of the game, open the game, open the save game and then create a new save game under the updated version.