Module development and code questions

Here's the code:

Hello everybody!
I am working on website using Drupal. I have done a lot of things using it. Now working on my own custome module. This module gives simple CRUD (Create, Reterive, Update and Delete) operations to just meet the requirement. Now the problem I need to improve the functionality of this module. I have to implement xajax to make it more interactive. But after a long search and effort could not find the simple search like This .

helllo everybody,
I want to display one images on the right hand side of the site logo but as i new to drupal i an not finding about any idea how to solve it please help if any one know........

With the taxonomy_access module, I can control the read, update, delete, create and list permissions. The read, update and delete permission work well without any problems. The only problem is with creating a new node.

Google recently added the ability for "Adsense for Search" results to be diplayed within an iframe on your own website.

Unfortunately, it doesn't seem to work within Drupal, because Google sends info back to your custom search page with a GET request, which includes the search terms as "q=your search terms". Drupal sees the "q" and tries to find a page with that name, returning "page not found" (unless you happen to search for something like 'admin' or 'user'). The result is the same whether or not clean urls are enabled.

1.) When I add assign a new node to a category, a new menu item will be created.
2.) I will go to admin/menu, and i delete this new menu item. Everything goes fine untill here, the menu item is gone as espected!
3.) Only when i update the created node, you get a sql error..because the menuitem will be created again. But the record in the category_menu_map table is still present, so it's a duplicate entry.

user warning: Duplicate entry '93' for key 1 query: INSERT INTO category_menu_map (nid, mid) VALUES (93, 350) in.