I didn't play the demo, so I'm not sure if save files from the demo carry over to full version or not. But if you start a new game, you do have to finish chapter 1 before getting to play chapter 2.
(There is no 'skip to chapter 2' button on the menu)
You're correct, and we will add that demo saves are compatible with the early access game. There's some bugs that may pop up from loading very old demo saves, but the save files are all still accessible.
Yes, Chapter Two continues directly on from Chapter One. Demo saves do carry over, so if you have a save close to the end of Chapter One from a demo, you can load it in the 2.0 version and simply continue.
