I'm going to jump on that third one and go with the Occam's Razor explanation.

Thanks to the epic Reset Button ending, nothing Blaze did in that game/time line ever happened.

Ever.

Period.

Or, if you want the not-so-simple explanation, how about this: The 06!Blaze was the ChaosWorld's Blaze, whereas Rush!Blaze is the SolWorld's Blaze, thusly making them two different Blazes.

1) How DID Gerald get the video of his execution to play when the ARK's deadly laser was activated. He was in Prison Island, you could see it. Did GUN help him carry out his plan? Did Shadow find him, recieve the instructions and steal GUN's archive video footage but not rescue his creator... geez. What the heck?

Well, he did tell GUN his plan; they recorded before executing him. Being a typical government agency, unable to reverse what Gerald had programmed into the ARK, they covered it up until it was pertinent, but when the colony began careening toward the Earth, they released the video, playing it across all of Earth's communication. The ARK, still connected to it all thanks to Eggman and his televised threats, picked it up.

*fap fap fap*

2) In Sonic Battle, Amy wishes so hard that Sonic would protect her that he appears to beat up Rouge (fairly difficult battle, too), after the fight Amy is suprised to notice that Sonic wasn't really there. WHAT THE CRAP?! He's real enough to punch Rouge in the face.

The way I see it, either the game was playing a sick joke on the players or Amy has the hidden ability to make anything she imagines become real, ala Foster's Home for Imaginary Friends, except she wouldn't have any memory of it at all.

I've got one thing to add to this whole fap, too:
The "WTF" Moment of Sonic Rush Adventure: At the end when Super Sonic and Burning Blaze have the Egg Wizard on the ropes, just as Nega is about to fire the "Planet Buster Laser" using the Jeweled Scepter, A small green orb of energy comes out of nowhere and hits it, distracting the Eggmen. You then see a close-up of Marine with some sort of aura surrounding her hand. There has been absolutely NO EXPLANATION concerning it at all. So here's my question: does Marine have some connection to the Power of the Stars the Eggmen were after or super-secret ninja tanuki abilities?

Random water hadouken.

yeah man those tanukis are mighty

nook burned my house down once by staring at it

I always figured that Gerald had given instructions to Shadow on what to do and carry out his revenge. Saving him, however, wasn't on the list, because, having lost Maria, he WANTED to die. Instead, he had Shadow... somehow get the tape of the confession of his plans. I guess Shadow hacked in and taped it for its intended purpose, while the people at GUN just thought he was loony, and only humored him because, well, he was clearly on the electric chair. Still, not willing to take chances, they captured Shadow and put him in cryostasis or something - which Eggman woke him up from shy of 50 years later. Shadow then proceeded to finish setting up the trap under Eggman's large, pink nose, intent on fulfilling Gerald's orders, thinking that was what Maria wanted. He was almost successful, too, until Amy jogged his memory of what Maria actually said that night.

You want a challenge? Well, given that working all the Zelda games into one timeline counts, then how about trying to fit SatAM in here somewhere? My best attempt involves making "Planet Mobius" into "Mobius Island", a detail never stated in the series, but which makes it a lot easier to believe (yeah, because you can conquer an entire planet by overthrowing ONE city). Plus it would mean that the series taking place on Earth later isn't a giant contradiction that would make even the least hardened defense attorney explode with sheer desire to point out.

I think the best fanwank for Mobius is what Sonic X proposed. Humans didn't show up until Sonic Adventure, anyway (excluding Machine King Ikkumon) so an unmentioned dimension switch may aswell be a definitive way to make all Mobius/Earth stuff canon.

I mean, obviously, I despise such stupid ideas and never would accept them in my own head-canon, but they are easily explained for those who want that imagination real estate.

2) In Sonic Battle, Amy wishes so hard that Sonic would protect her that he appears to beat up Rouge (fairly difficult battle, too), after the fight Amy is suprised to notice that Sonic wasn't really there. WHAT THE CRAP?! He's real enough to punch Rouge in the face.

I thought that whole fight was in Amy's head. As in Amy is daydreaming about Sonic hitting Rouge, just like all good romantic daydreams, while real Rouge is just standing there wondering what the hell Amy is doing. Ages since I played the game though.

3) Okay. Blaze. She exists in the crazy future of Sonic 2006 but she is the princess/queen of Sol world and keeps the Sol Emerald's and knew nothing of Earth. What gives?

Sealed in another dimension, in Silvers ending... but that ending was in a timeline should not have existed because Elise did not die, Sonic saved her. And that timeline was erased anyway due to the whole endgame... yes the right question for a fanwank topic.

...So I guess the key event of the dimension swap stuck, but due to the fact the timeline got erased Blaze had no memory of it. And she came back to 'the present' rather than the 'future', because the Solaris fight took place in Sonics time?
Thus Blaze, someone with fire powers, awakens with Amnesia in a place where 7 'fire gems' are (I guess) the most powerful things on the planet. The people of that dimension notice the fire conection, and end up making her guardian... the Princess gig comes with the job, due to the importance of the Emeralds?

Speaking of Futures, Alternate Dimensions and the like...

What is the deal with Eggmn Nega? Eggmans ancestor as seen in 'Rivals', or his alternate universe counterpart as seen in Rush? Or a bit of both, I mean Blaze has Sonics shoes, if he were an alternate gender, but she is from the future. Shoes are important people!

I think the best fanwank for Mobius is what Sonic X proposed. Humans didn't show up until Sonic Adventure, anyway (excluding Machine King Ikkumon) so an unmentioned dimension switch may aswell be a definitive way to make all Mobius/Earth stuff canon.

I mean, obviously, I despise such stupid ideas and never would accept them in my own head-canon, but they are easily explained for those who want that imagination real estate.

Except Sonic X never explains how Gerald knew about the Chaos Emeralds.

*fanwanks until fangoos all over everyone :P*

I thot Gerald was fake and Blacky Doom did everything o.o at least the video

The eye could have too. ZIRCON *slams staff into the ground*