1. According to this page on Amazon.com, FireRed and LeafGreen were the first games to use the Wireless Adapter. Thus, I doubt you'd be able to use it on Ruby and Sapphire. However, you can trade between those games with a Game Link Cable. I'm not sure on Emerald, though, and since I should be studying right now, I won't do extensive research for the time being.
2. Since you can use it to trade between a "return to Kanto" game and Ruby/Sapphire, I don't see why you wouldn't be able to use it between two of the "return to Kanto" games. Not sure, but that's what I would suspect.
3. Unfortunately, as I've said in this topic, it doesn't look that way. The two systems just don’t seem to have the same types of ports. Sorry.
And congrats on your new puppy!