The errors depend on you server etc.
e.g. with apache you can use .htaccess files to redirect certain erros to the registration page.
Here is an example from my file:
ErrorDocument 404
http://www.able2know.com/forums/profile.php?mode=register&agreed=true
As to the quick registration form just make a template (start with your profile_add_body.tpl) with the items you want on your form and name it 'profile_register_body.tpl'
Then in includes/usercp_register.php
find
Code:
$template->set_filenames(array(
'body' => 'profile_add_body.tpl')
);
replace with
Code:
if ($mode=='register')
$template->set_filenames(array( 'body' => 'profile_register_body.tpl'));
else $template->set_filenames(array('body' => 'profile_add_body.tpl'));