That's a TV theory because the actors playing J and M look like they could be related. They look nothing alike in the books, I'd be shocked if it were true. I wholeheartedly agree with R+L=J though and it's practically confirmed now.
IMO, it's more than just the strong resemblance between the two actors. It's no coincidence that Howland Reed is the only other one besides Ned to survive the battle at the Tower of Joy. That puts him right there in position to help. And we know twins run in the Targaryen bloodline. And her character is about the right age and seems to be waiting in the wings for something to happen, always just offscreen but seemingly important.
Definitely could be wrong but seems pretty plausible to me.
Maybe, but I don't think so. R+L=J has been a theory since GoT (the book) first came out as the clues were always there. There's nothing IMO that suggest M is a part of it in the books. Like I said, it's more a TV theory because of the likeness between the two actors and I really didn't see this theory grab a hold until the TV show came out. Trust me, the hard core ASOIAF dorks would have figured it out long before the TV show became a reality. Now, GMMR could add it in later, but I've read he isn't going to change something because the nerds figured it out. I'd have to trust him on his word.
Now, I believe HR has a big part to play, either by directly saying R+L=J is true, or confirming it once someone else finds out. How, I have no idea, but he's been mentioned too much to be a coincidence.
And the Targaryens aren't known for twins, they're known for marrying their siblings and having multiple marriages. Off the top of my head, I don't recall any Targaryen twins, but granted, there's a **** load of them mentioned in the various works. The only prominent twins are Cersi and Jaime (and Frey's castle, if you want to get technical).