Read the messages again; it tells you exactly what it is trying to insert and where. My question is why the Embed Video module is mucking with the menu system; that's either something you messed up in the settings somewhere, or a serious bug in that module. Either way, open an issue.
 
For performance, I always start with the Devel query log. There is always at least one module that is doing far more queries than it needs to. Open an issue to get it (or them) fixed.
 
Make sure anonymous caching and CSS compression are turned on. Check for the Statistics module - do you really need it? And evaluate the need for the access log. While you are playing with Devel, turn on the error reporting; you will find other errors that don't normally get reported, but are slowing you down anyway - report them.
 
Check that query caching is turned on and set at a realistic size - go to your status report and click on the MySql release number for stats on the database.
 
Nancy
 
Injustice anywhere is a threat to justice everywhere. -- Dr. Martin L. King, Jr.

From: robert mena

 
My question is I don't see why I get so many errors, specially those DUPLICATE ones.   This should be a starting point but again I do not see what is trying to insert and how to solve it.User warning: Duplicate entry 'admin/content/node-type/news/fields/field_embed_others_video' for key 1 query: INSERT INTO menu_router (path, load_functions, to_arg_functions, access_callback, access_arguments, page_callback, page_arguments, fit, number_parts, tab_parent, tab_root, title, title_callback, title_arguments, type, block_callback, description, position, weight, file) VALUES ('admin/content/node-type/news/fields/field_embed_others_videos', '', '', 'user_access', 'a:1:{i:0;s:24:\"administer content types\";}', 'drupal_get_form', 'a:3:{i:0;s:23:\"content_field_edit_form\";i:1;s:8:\"news\";i:2;s:25:\"field_embed_others_videos\";}', 63, 6, 'admin/content/node-type/news/fields', 'admin/content/node-type/news', 'Embed video', 't', '', 128, '', '', '', 0, 'sites/all/modules/cck/includes/content.admin.inc') in _db_query() (line 136 of/public_html/drupal/includes/database.mysql.inc