Disable "Log Out" and 2nd mouse button?

Yesterday my wife and I switched her grandfather from Windows to OS X on a Mac mini. He is a little nervous about using a new OS and he thinks he's going to screw something up (I doubt it). We've run into two problems.

1) He keeps trying to Shut Down but instead he's logging out. We clearly explained to him and demonstrated to click "Shut Down" but he keeps going to the bottom and logging out. Is there a way to remove "Log Out" from the Apple menu?

2) He is using a third party generic two button mouse. He likes it and wants to keep it. However, because he is older and his hands are a little less flexible he tends to paw the mouse. In doing so he inadvertantly clicks the right mouse button a lot, opening the contextual menu. That screws him all up. We've explained it to him and he understands somewhat to try not to click the right button, but he still does sometimes. I went into the Mouse Preference pane but I can see no way to disable the 2nd mouse button.

Thanks in advance,