Petunia (what's Up With Her?)

What's the deal with Petunia?
I know that we're not done with her, but I can't guess how it will go.

Maybe one of her parents was a squib,
and a grandparent (Harry's great-grandparent) was "RAB."
And maybe he knew about the prophesy.
Rowling likes to take strange turns like that.

Nah. Regulus Black & Kreacher are still the most likely "RAB" suspects.

Kreachure... why do you think it is him? I never thought of him... but I'm not quite sure why it would be him...

Black's little brother (Regulus or something like that), because he had a grudge against Voldemort. Kreacher because the second person in the boat could not have been an adult wizard. And someone on this board said something about a locket in the Black's house that no one could open.

Don't forget: We know that items from the Black house were stolen and being hocked by Mundungus Fletcher.

it's a possibility that it was taken by Regulus Black. it is possible but if it is him, his middle initial would have 2 be 'A'. it said that the note that Harry found in the fake Horcrux was signed 'R.A.B' and there could be hundred or thousands of witches and/or wizards with those initials. but in book 5, Sirius explained 2 Harry that his lil bro Regulus Black had a grudge against Voldy. if it was him he could've stashed it at #12 Grimauld Place b4 he was personally murdered by Voldy. and since Mundungus Fletcher had stolen a bunch of Sirius' stuff, he could've stolen the locket, but only if it was Regulus who got it and he had hidden it at #12. and therefore Mundungus could've sold it 2 anybody, so it could be anywhere. if that is tru then this might take a while.

Is it possible that Petunia is magical but refused her invitation to Hogwarts?

If that were the case, would she has any powers at her age with no training or use?

I think it is unlikely that Petunia has any magical powers. Lilly's parents were both muggles, Lilly is a "mud-blood" like Hermione. And I think the odds of two muggle parents producing two magical daughters is pretty slim.