Do all character cards, assets, skills, weaknesses, etc enter the general card pool for deckbuilding? I mean can I use Dunwich Legacy cards for the core scenario or even for other deluxe expansions in the future, and vice versa?

Yes. Just how you can use Magic The Gathering cards from 10 years ago with modern cards. Or how you can use investigators from Under The Pyramids expansion against Azathoth when playing Eldritch Horror. It's called an "expansion" for a reason.