1) Submission deletes existing categories and doesnt save new values.
action.fesubmit.php line148

if( isset($params['cgblog_category_id']) ) $category_id = (int)
$params['cgblog_category_id'];

should be

if( isset($params['cgblog_category_id']) ) $category_id =
$params['cgblog_category_id'];

(value should be an array not an integer.)

2) Blog Edit Form doesnt mark checked next to existing categories:
orig_fesubmit_template.tpl line 36

{if in_array($node.id,$sel_categories)}checked="checked"{/if} 
should be
{if in_array($node.id,$sel_categories[0])}checked="checked"{/if}

Regards