Well, HPL's work on the Mythos is in the public domain but Chaosium's RPG is not. Much like Arkham Horror itself is not. In order for FFG to borrow material from the CoC RPG, they'd have to have some sort of agreement with Chaosium. That would involve fees and contracts and a bunch of other red tape they can avoid simply by sticking to what's in HPL's public domain writings instead. This is not to say it's impossible they might take scenarios from the RPG, but I suspect it's unlikely.
Unless the font for "Mansions of Madness" is the same in the RPG, I'd be inclined to say it's a generic enough title that FFG could use it without owing anything to Chaosium for using the same name.
I don't remember the characters of Mr Corbitt or his son, personally, so I don't know if they're part of the Mythos or something invented for CoC. If they belong to HPL's body of work, then FFG could very easily use them, too. Assuming both CoC and FFG are working from the same story to create their independent scenarios, you might end up with something very similar, but probably not identical. If they were created by Chaosium, they almost certainly will not appear in FFG's game. Unless FFG and Chaosium have actually signed on to work together, of course, but again I think that's unnecessary and thus unlikely.