Hi
You need to have 2 search modules.
One published on "header3" module position and assign to Home.
The second published on "search_bottom" module position and assign to all, except to home.
About the rest module positions, you can check the Helpfile of Coolfoto template and check all the modules positions set on the demo... but of course, the best way to start your own website from zero was to install the quickstart version, like Teibite said.
Cheers