Unfortunately can't open the link at work.
However, while teleport can get around the solid wall of the worm's stomach, it won't get around the line of sight/line of effect issue. I would still argue that he could not teleport the target (usually these powers also say "1 target in burst you can see"). Obviously I can't see the actual wording yet but I would think that he's out of luck on the swallowed PC.
As to the invisibility, again, I think you made the right call.
However, I also think that both you and the bard have issues that should be addressed. The bard gets lots of little tricks, but none of them are really game-breaking. You talk about the bard imitating a dragon call, but really, any character can try that, its just that the Bard was the one that thought of it. Additionally, on that note, I would also argue that the party defeated the encounter, they just did it in an unanticipated way. I would certainly give them credit, and XP for that. Think of it this way, if the fighter comes up with a scheme to collapse the ceiling over a room full of orcs, do the orcs not die, and more importantly, does the party not defeat the challenge? In both cases, I would award full XP and thank the heavens that my players are creative.
I'm not sure what your complaint with the double D-20 is. Do you have a house rule that grants an auto-kill on a double nat 20 roll like the optional rule in 3.x? If so, this is again, not a bard issue, but rather a rules issue that can affect anyone.
I think the bard's player is trying to get the most out of his powers, including to the point that he is trying to bend the rules more than just a bit. In the end, I would sit down and talk to him. Praise him for his creativity but also explain to him how the mechanics work -- according to your ruling. Ultimately, you as the DM are the official arbiter and the rules in the books are really just guidelines. At the same time, I would also tell him that if this affects his desire to take this particular power that he is free to change it out.