Changing the title of the advanced search can be done with the translation feature, just create a CSV file in your magento locale theme directory.
By default the theme is default/default and can be found in app/design/frontend/default/default.
Example (Assuming your store locale is English (USA) and you’re using the default magento template):
create the file app/design/frontend/default/default/locale/de_DE/translate.csv and plache the following line there (no trailing or leading linebreaks/whitespaces):
“Catalog Advanced Search","Advanced Search”
Flush the magento locales cache and thats it.
To change the url from /catalogsearch to /search is pretty simple, just login to jour admin pannel and navigate to “URL Rewrite Management” in the “Catalog” Menu.
Add a new URL-Rewrite by klicking on the appropriate button, select type “Custom”, enter a unique id-path (i.E. ‘custom/catalogsearch’), select your store view, enter ‘search’ in Request path and ‘catalogsearch’ in Target Path.
Save and you’re done