The VG Resource

maybe this can just not be a working mario kart sprite? idk.

I like it. A lot.
On the first robotnik though, I notice that one of his eyes is a pixel or two bigger than the other.
And on the modern one, his moustache is.. unshaded. Other than that, though, this is cool.
When you described the three different styles as "modes", do you mean that they're all different characters in themselves, or that they're just, palette swaps, so to speak?
If so, you should edit the first robotnik to have the same design as the sonic 1 eggmobile, the second.. i don't really recall what the AoStH eggmobile looked like, and for the third, you should leave it like that, it looks modern that way.
Other than that... keep truckin' on it. It looks nice.

Edit-
The first one's eggmobile is perfect. The other two's are the ones you should rearrange. Sorry about that.

Edit-Again-
Nevermind the thing about the first Robotnik's eye... i dunno what i was thinking on that one. It's perfect.

Thanks, I'm glad you like it.
Well, I don't exactly know what to do with the eggmobile, because it's based in Sonic 1 sprites, and the AOSTH uses the same one, and, as far as I know, modern one is the same or at least very similar. I supposed them to be like pallette swaps, but not only pallettes, like different suits.
Now it doesn't look accurate because it's front pose, but when it's 360 degrees it will look good.
About the moustache...well, I wanted to use color restrictions, and in the first two the shade was already there, but in the third one it would need a new color, and I don't know it that would pass color limit. Well, I could lighten modern one's moustache, but it wouldn't be totally accurate.
About being bigger than supposed...I don't expect this to appear in the actual Super Mario Kart, it's obviously impossible, but I've checked fangames and they use bigger sprites, for example, the SMK Petey Piranha.

Have you considered using the Game Gear Sonic racing games as visual examples for this project?
Sonic Drift and Sonic Drift 2 were such blatant Mario Kart ripoffs that you could turn that into your advantage here.

Oh thanks, I'll look at them.