to get the buttons back, right click in a blank area up the top and click customize. then you can drag and drop the buttons where you want them.

the private browsing basically starts a new browsing window, seperate from what you were browsing before. in private browsing, you dont want it to remember history, so it doesnt 'mix-in' with your normal browsing history, otherwise it would have to wipe the lot. you can still go forward and back in private browsing, but only on pages you visited whilst private browsing. so you could always browse privately, if you wanted complete forward and back control of all your pages.