Snake is Smash Bros Snake because he is a combination of Solid Snake's costume and Big Boss's facial features.
Sonic doesn't have "incarnations" and borrows elements from the character's history, so yes, he is Smash Bros Sonic.
And Classic Mega Man has never been rendered in 3D.
Samus and Ness had never been rendered in 3D before Smash 64. That doesn't make them "Smash Bros Samus" and "Smash Bros Ness". Mega Man was also rendered in 3D in Mega Man Powered Up for the PSP, which is a remake of the original Mega Man. So no, it's just Classic Mega Man.
Sonic has many incarnations, but the one referenced in Smash Bros is the most widely known one alongside Classic Sonic. However, Modern Sonic is still capable of doing everything Classic Sonic does, and they are confirmed to be the same character. So no, it's not Smash Bros Sonic. It's Modern Sonic.
Solid Snake is a clone of Big Boss, and could easily grow his facial hair. Also, Snake in Brawl can communicate with characters Solid Snake knows on his codec, but Big Boss doesn't. So no, it's Solid Snake.
Also, the character bios in the game do not list them as different incarnations of the characters. They are literally the same characters, as we know them.
She doesn't work against the standard, she gives evidence to the only standard that exists; and that is the one that lies with Sakurai's discretion as developer. Trying to cherry pick an arbitrary evaluation to cast a negative light on Paper Mario when there is already evidence to the contrary. Many of the same arguments against Paper Mario were used against Rosalina, yet Sakurai found an interesting way to implement her that makes him look like a genius, and all of us silly. Paper Mario has that same potential. That's all I'm trying to say. Not trying to do mental gymnastics.
No, she doesn't work against the standard. The standard is that a character must have appeal of some kind. Wii Fit Trainer had that, and that's why she got in. Sakurai conceived the idea of Smash because taking APPEALING and BELOVED characters and putting them in a game is a fun idea, and he has said this is the essence of the franchise himself.
Also, the Rosalina naysayers were people who hardly get the character at all. I've always seen potential for her, since Brawl, and many others rooted for her inclusion. People stereotype her as "Emo Peach", but it's not what the character is at all, and she had already established herself as a distinguished character. She was not literally Peach. Paper Mario is literally Mario, and Mario can do anything Paper Mario can.
Yeah. I mean, even with Toon Link, if you want to get nitpicky, he can't actually jump that high in Wind Waker, and the upward and downward stabs are moves from Adventure of Link.
Actually, Toon Link in Wind Waker could jump WELL over the heads of characters much taller than him, and he also performed the downward stab move against Ganondorf.