Re mechanism.
Hydrogen peroxide can exchange peroxide linkages. If so, then cyclohexanol can form the peralcohol. This can decompose to cyclohexanone by loss of water. Most oxidations progress via a loss of HX from a R2CHOX to give R2C=O. Addition of hydrogen peroxide to cyclohexanone can give the lactone via a Baeyer-Villiger reaction.
To get adipic acid, open the lactone and repeat oxidation of alcohol, aldehyde to acid, and ta da.