For your first question, all he is doing is edgehopping and shooting a beam. To edgehop, yo ulet go of the edge (Hit back or down on the control stick), and then immediately jump and shoot the beam. The lag from the beam will finish in time for you to grab bcak onto the edge and repeat. Samus can also do this with bairs, uairs, and sex kicks (although sex kick are harder to do).
Secondly, I'm not sure why you wouldn't be able to platform missile cancel on pokestadium, the only thing I can think is if you are starting the missile late, especially when doing a homing one, so just try to shoot the missile earlier.
As for Dreamland and Battlefield, there's a bit of a difference when you need to platform missile cancel. Instead of doing a shorthop, you have to double jump in order to get enough height. So what you do is jump, and then as soon as you're in the air, jump again and shoot the missile. Since when you double jump makes you go different heights, the closer you double jump to the first frame that Samus is airborne, the lower your jump will be. However, since any double jump makes the platform, trying to double jump perfectly is the fastest way to do those.
It's a little harder to learn and pull of consistently in place, but there are a bunch of setups you can use for it. Phanna rolls his thumb from Y to X and then moves it over to B to do this. I do something similar, but roll my thumb from X to Y to B, as it seems like more of a circle. You could also try X or Y to jump first, then use the control stick for the double jump an droll it forward to shoot the missile, but I've found that it sometimes results in accidental upBs.
I'm not sure if phanna has this problem with hi method, but with the way I do it (roll thumb over X to Y and then hit B) I sometimes hit A, since I'm rolling my thumb right around teh button and trying to go quickly. I think what it might come down to is whether you normally use X or Y to jump, as that should be the button you use for the second jump, as it'll probably feel more natural to you.
Oh, and you can also jump double tap X or Y, although in all likelyhood, that would be much slower than rolling your thumb or using the joystick.