Hey that little man can be quite helpful if you give him half a chance... I use him as a shortcut for the screen magnifier lol.
On a serious note, go to settings-accessibility and make sure nothing is activated to use a screen button or shortcut... which is what the little man is.
For the navigation buttons go to settings-system-gestures and turn off 3 button navigation. You'll have to use slide gestures though, so be aware of that.
I would think the buttons would disappear in a game though.. similar to when watching a movie or something else where the buttons would be in the way? Maybe it's a game setting of some type?