Custom styling and positioning of 'search block'

I have a developer site and have added the 'search' block to my site. What I want to know is if I can now completely change the CSS of the search block? And by looking up the CSS classes of the search block and over-writing them, what CAN you change?

Also, how would I be able to put this search block in my 'navigation.block' file?

Thanks in advance!