Hi Jason,

Regarding the user text avatar image, currently there is no option to configure to use 32x32 dimension. What you can do is to modify this file 'JOOMLA/administrator/components/com_easysocial/includes/textavatar/textavatar.php' and change the text avatar size at line 74:

$image = imagecreatetruecolor(SOCIAL_AVATAR_SQUARE_LARGE_WIDTH, SOCIAL_AVATAR_SQUARE_LARGE_WIDTH);

To:

$image = imagecreatetruecolor(SOCIAL_AVATAR_SMALL_WIDTH, SOCIAL_AVATAR_SMALL_HEIGHT);

Remember to backup the original file before you modify to use small size dimension.
Anyway, have you consider to use pagespeed to compress the images so that the image load time will be faster?

As for the ETag issue and the cookie-free issues, its more on how you configure your server to serve the static content. For cookie-free, you can try with CDN or any similar service provider so that your images are serve from these cookie-free server.

Please advise.

Hope this help and have a nice day