Peroxide in acidic conditions being reacted with iron sulphate mechanism For the proposed mechanism, I would like to think the $\ce{O-O}$ bond would be cleaved first, thus creating two radicals (an $\ce{OH}$ radical and the radical situated on the other Oxygen), then radical on the oxygen will go into the ring to form a double bond in which the alkene double bond will donate 1 electron towards that bond and 1 electron to the carbon on the end of the opened ring.
My mechanism would be incomplete as I cannot seem to figure out how this reaction occurs.
However, I have another suggestion in which there is an epoxide formation. Can anyone elaborate as to which one is correct or can give me some insight?
At least for the second part of the product formation, you have pretty much given the answer yourself.

The methylcyclopentane moiety of the products results from two different 5-exo-trig radical ring closures, that is from the intramolecular addition of two different radicals to $\ce{R-\color{\red}{C}H=CH2}$. 

How are these two different radicals generated?

Have a look at the starting materials! Isn't the combination of the hydroperoxide $\ce{R-OOH}$ and $\ce{FeSO4}$ very similar to the conditions of a Fenton reaction?

Let's therefore postulate the following: $\ce{R-OOH + Fe^2+ -&gt; R-O* +\quad{}OH-  + Fe^3+}$

The resulting 1-methylcylohexan-1-ol derived radical can form methyl ketones by cleaving two different $\ce{C-C}$ bonds; the resulting carbon-centered radicals then give rise to the different cyclization products.