title says "Hide profile2 and captcha label in registration form" so how come my answer doesn't answer the question?

probably you doing something wrong check how is it done check these link maybe it will helo morelink link

for me it all works fine. if you set $variables['appcache'] then in html.tpl.php $appcache is available. just put die(); in your your_theme_name_preprocess_html and see if it called. maybe you need to clear theme cache

what exactly doesn't work? where did u put your_theme_name_preprocess_html ? did you rename your_theme_name to you theme name? and did you put it in template.php? is that function called?

yes. you need to create region--header.tpl.php but not region.header.tpl.php you can copy and rename modules/system/region.tpl.php but then you need to remove div wrapper from there