To loop, you can add the composition multiple times, or you can pre-render the comp then reinteprete the footage to turn on looping.
Select your nested comp and choose Layer -> Time -> Enable Time Remapping.
Expand nested comp layer as needed (e.g. go to the end of the master comp and press Alt/Opt + ] with nested comp selected).
Alt/Opt + Click on the Time Remap properties of the nested comp and add the loopOut("cycle") expression.
there's also the
loopOut(type = "cycle", numKeyframes = 0)
script that you can add to the comp.