What I don't like about it, is that when I click on the search bar (double click in it) or type in a letter it starts to drop down a menu and show my past search queries
You can remove that feature by adding autocomplete="off"
to the control.
Is there a way to replace the suggestions with a customized list of tags, or the one like Youtube which shows up a list of suggestions based on popularity and not include searches from external sites?
Yes, but you have to custom build it with an element to hold the results and the server-side code to populate the suggestions.