They do not come apart from the rear. I believe if you pry out that plastic dust shield, you'll have access to the outer cone for disassembly.
Freewheel disassembly can be tedious, and it may not be worth doing to some. I don't mind doing it, and I've done several from various manufacturers. Here's a link to a thread where I cleaned one up:
https://www.bikeforums.net/classic-v...freewheel.html
And yes, keep the pawls grease-free or they'll stick.