How do you turn off the suggestions form the google search bar?

You can't turn off the suggestions in Safari, though you may be able to do that if you install Glims, which also offers some additional options that aren't available directly in Safari.

Quit Safari before you install it, then restart and go to Preferences>Glims to setup your options.

As for drop-down boxes, what exactly are you referring to?

Google itself is doing this, not Safari. If you go to Google's main page and start typing you will see the same thing happening. So maybe some third party hack can stop it or maybe not.

There are no toolbars that are for Safari, which is what your post is about. So the search suggestions are when you type something into the Google search field in Safari, and you cannot turn those off within Safari.

If you're referring to the Google web site, that has nothing to do with Safari, in which case you should search Google Help for a solution.