"Will Complete Cleanup remove the previous search engine entries I have done? Will it also clear the previous text that was entered on various websites?"

Complete Cleanup will safely clear all the previous entries and searches you have done. These are called "Auto Forms" and you can use the button that says this (this feature is currently only on the registered version). It will remove any previous information including passwords, text, search engine entries, text box entries, and any other information that you have previously entered on any website.