Buying the game in Early Access on here or on Steam will mean you'll get the rest of the chapters as they release (you may need to manually re-download the game if you're getting it here on Itch), so no worries on that front.
The demo save data does carry forward into the main game (provided it's all on the same device, I should say!), so you should be able to continue playing without issue. If you're download the game files here on Itch, you won't need to fold onto the demo game files afterwards. Ren'py saves the game data in two places on your computer, and the demo and main game both check the same folders for save data, so everything carries over.