I would question whether an eight year old should be driving at garden tractor at all but if you've made that decision he should be supervised at all times and all the machine's safety systems, such as the seat pressure switch should be fully functional . If it has not got a seat pressure switch or it has been by passed, that should be rectified. Consider a "kill tag" that cuts out the engine should he fall off or hit his head on a tree bough etc.
While anything is possible I think that the installation of a centrifugal clutch and additional brake will not be a simple matter. A tractor with hydrostatic transmission would achieve smooth single pedal or lever control of forward neutral and reverse and give dynamic braking.
A used transmission such as a TuffTorq K55 or 46 would fulfil both the above functions and is perfectly "doable" using readily available new and used parts. Alternatively re-sell the machine and buy a hydrostatic one.