1. Previous saves won't work, starting a new save is needed.
2. Yes, you can disable the cheat menu, trigger the extra scenes and then enable cheat menu again.
It's the lack of framework and design when creating a new game and making up stuff as you go. The biggest issue is adding new characters later, all of which require new variables, which aren't present in the old saves. That's the reason why they aren't compatible. So in a way it's not purposeful, but it's a bad biproduct of developing game this way. Dev has said that as of v0.7.8 there won't be major changes, so in theory saves should work with the future updates, but take it with a grain of salt.
No, I don't think so.
No.