Does anyone have suggestions on places that provide in depth site / analytics reviews for SEO?

Is it common for a site to see slight traffic drops after a site redesign (containing cleaner code, more usability and basically just being more helpful for the end user)?  A new site of ours went live last Wednesday and has experienced a drop in traffic. If you have seen this in your own site, how did you recover? And how long did the recovery take?

I have read that loading images from a subdomain of your site instead of the main domain will give you speed benefits on load time. Has anyone actually seen that to be the case? Thanks!

I am working with a per page results refinement that stores a cookie on the users computer and then keeps that same per page as the user goes around the site. I was just wondering if that was true for Google bot or Bing bot as well. Will they keep the cookie or would they not be able to accept it. I just want to know as I dont want different urls created if they can keep the cookie. Thanks!