To both your questions: Yes.
Wheel and Staff are both a part of an OS X system. Now you know - don't mess with them!
Don't manually change random permissions and ownership on anything, unless you know what you are doing, or have clear direction on what to do. Your wife might not be the "expert" that you need to ask about this stuff
There's a few here who often will answer back more quickly than you might expect.
The OS X reinstall will fix all those important system parts, and get Wheel and Staff back in their proper places.