Does the Tegra Note support apps to SD in stock form?

I've had no issues moving apps to SD, including huge ones like Asphalt 8. As for the Moga Pro, I have one, and it works just fine, though if by "fit" you mean physically fit in the clamp, no, it's way too large for that. Luckily your Moga Pro should have come with a tablet stand, or at least mine did.

There's no Console Mode yet, so it just simply mirrors the 720p output of the tablet's screen, and since the tablet is actually 1280x800 and not 1280x720, there are small black bars on the left and right, and for some reason the top and bottom are slightly cut off on my TV. Even with those little issues, it basically works like you're playing a console, and unlike other Android devices I've hooked up via HDMI, there's absolutely no slowdown and very close to no lag... it's easily the best HDMI-out experience I've had yet with Android. Once Console Mode is implemented (it had better be with the 4.4 update!), games should be able to output at 1080p and will hopefully fit the screen a little better. For the record, if you watch a 1080p video, it'll switch the output to 1080p, but it only happens in that one instance for right now.