Misuse and Abuse

...under public scrutiny and avoid misuse of power

...under public scrutiny and avoid abuse of power

what's the different between them?

In this particular case, there isn't much difference. The two words are not always interchangeable, though. To misuse a hammer might be to try to use it to pound in a screw instead of a nail, but to abuse a hammer would be to damage the hammer.

- Kef

The second one is more common.

Can we say "the physical misuse of children"? If no, why?

To "misuse" a child, there has to be a meaning to "use" the child in the first place. But you can't really use a child in that sense... you don't "use" a child the same way you use a tool or a privilege.

- Kef