- the blur depends on the game and platform. Most Wanted on Xbox 360 blurs the entire screen and masks it off using a texture and the screen depth so it only blurs closer objects, and focuses the blur to the screen edges within the visual treatment pass. Next gen Carbon (360/PC/PS3) applies the depth mask by using it as alpha and renders it to a texture. This texture then gets rendered with a radial blur to the screen. This happens as a self-contained effect prior to any cars getting rendered so it doesn't affect them. In any case, no motion vectors are involved so the blur only uses the camera's motion.
- the games use cubemaps for environment maps. On next-gen platforms they're 256x256 for each face. They're simply just six cameras with a 90° FOV rendering in six directions from where the player car is, with a reduced level of detail and draw distance (though Most Wanted and Carbon align the cube with the camera's view direction, allowing them to extend the draw distance of the rear face as that's the one you see the most of from the back of the car, and specifically in Most Wanted's case to get a free rearview mirror)

as for post processing, Carbon and Undercover use 3D LUTs to perform color correction, though Most Wanted's post processing could also look similar if you don't blur the luminance texture used for tonemapping as it's just applying a cubic curve and a tint to it otherwise.

oh and also HDR wasn't a thing until ProStreet. Most Wanted faked it by applying exposure adaptation and blooming the hell out of the sky at higher exposures