To remove the Web / Site search options edit your skin's .ascx file as follows:
<dnn:SEARCH runat="server" id="dnnSEARCH" showWeb="False" showSite="False" />

To change the Web search to use your Google Adsense key:
edit   \admin\skins\App_LocalResources\Search.ascx.resx 
change the value after pub- to your Google Web Search Id
<value>http://www.google.com/custom?hl=en&client=pub-9770992166002654

Read more at:
http://blog.scottschecter.net/2007/05/30/DisableNewSearchFeaturesInDotNetNuke452.aspx