About halfway down you'll see the find() function. I wouldn't have a clue how to use it though - maybe one of the other brains around here can give some advice on that! ;)
Incidentally, you are aware that this will only search the current page, right? If you want a true "site search," you need to find an actual script to use. If that's what you're after, I can recommend Perlfect search as being easy to set up and use.
I highly doubt it's possible. Besides, I have my Firefox set up so that I just type a word directly, and it's highlighted on the page, without me ever seeing a Find box. All browsers work differently, and not all browsers use Ctrl+F to launch the find... Indeed, there may be browsers that don't have find at all.
Oh, and I'm pretty sure that AddFavorite isn't real code either...