show us detailed full screenshots and tell us what's wrong for you in what we are seeing.
About the colors:
1. Go to the swatch palate, into the generic "swatch options" menu and change CMYK to RGB
2.in illustrator export make sure this is unchecked: "Include CMYK PostScript in RGB Files."
About the pixels:
unlike Ai, Ae is resolution dependant. set you Ae magnification at 100% and you will see it sharp, unless some of the artwork is not falling exactly on the pixel grid and causes antialiasing which is normal if it's not straight vertical or horizontal lines. you could maybe adjust it a bit to fall right into place and make sure your position coordinates are whole numbers but if it's animating it will eventually get antialiased.
I see you are working in a 1000*1000 pixels composition. Unless this is your output, You might benefit from working from within the presets in Ai an Ae. Video has standards, the most common is HDTV 1920*1080.
If you are intending to export a compressed video to youtube/vimeo/any other, be prepared to be less critical on accuracy of vibrant colors. The chroma subsampling in compressed video formats will wash off some of really vibrant colors , and this is without mentioning the fact that browsers or monitors will look diffrent.
more reading material here: Preparing and importing still images in After Effects
Sorry for this issue. Did you ever find a solution? Please let us know if you have or if you still need help.
I have the same issue and nobody can give me a solution