Not if you paste it to your site correctly. I just paste the analytics code to my footer file that is attached to every page on my site. The script comes right from Google's content delivery network which will more than likely be faster than your own site since they not only deliver the script from the closest server to the user, but the code is likely cached anyway.

I guess if you don't paste the script correctly, it could screw up your site's appearance in theory, but you shouldn't have any problem doing this.

A) No, It does not affect your website's appearance in any wayB) It will affect performance unless you paste the analytics code right at the bottom of the page, so that it loads only after all the other elements have loaded. As a normal practice, all javascript should be loaded just below the end of the </body> tag